Demonstrations of locomotion capabilities of snake robots have been addressed by several researches. However, in most of the cases, human intervention is needed in the gait design procedure. For an experimented gait designer, a locomotion mode for a modular snake robot is a very intuitive notion. To put this notion in a more formal mathematical manner, some considerations must be taken into account. This paper proposes the mathematical representation of the different spaces of variables, related to the mathematical representation of a modular snake robot's locomotion. The mappings between these spaces are shown and explained with detail. Constraints of the parameterized space are presented, in order to define formally a locomotion mode. Experiments with several random predefined gaits, representing groups of gaits with common locomotion features, were used to classify these gaits and validate the locomotion mode definition.