Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a number field of degree at least <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="3"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding="application/x-tex">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this article we show that the genus of the integral trace form of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> contains only one spinor genus. Additionally we show that exactly <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="43"> <mml:semantics> <mml:mn>43</mml:mn> <mml:annotation encoding="application/x-tex">43%</mml:annotation> </mml:semantics> </mml:math> </inline-formula> (resp. <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="29"> <mml:semantics> <mml:mn>29</mml:mn> <mml:annotation encoding="application/x-tex">29%</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, resp. <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="58"> <mml:semantics> <mml:mn>58</mml:mn> <mml:annotation encoding="application/x-tex">58%</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) of quadratic (resp. real quadratic, resp. imaginary quadratic) fields have the same property.