## Defining parameters

 Level: $$N$$ = $$14 = 2 \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$1$$ Newforms: $$1$$ Sturm bound: $$36$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(14))$$.

Total New Old
Modular forms 18 4 14
Cusp forms 6 4 2
Eisenstein series 12 0 12

## Trace form

 $$4q - 6q^{3} - 4q^{4} - 6q^{5} + 8q^{7} + O(q^{10})$$ $$4q - 6q^{3} - 4q^{4} - 6q^{5} + 8q^{7} + 24q^{10} + 18q^{11} + 12q^{12} - 36q^{14} - 36q^{15} - 8q^{16} - 30q^{17} - 24q^{18} + 6q^{19} + 54q^{21} + 24q^{22} + 30q^{23} + 24q^{24} + 4q^{25} + 24q^{26} - 20q^{28} + 48q^{29} - 12q^{30} - 42q^{31} - 90q^{33} - 42q^{35} - 62q^{37} - 12q^{38} + 12q^{39} - 48q^{40} + 72q^{42} - 8q^{43} + 36q^{44} + 144q^{45} + 36q^{46} + 174q^{47} - 20q^{49} - 96q^{50} + 54q^{51} - 72q^{52} - 78q^{53} - 36q^{54} + 48q^{56} + 12q^{57} + 24q^{58} - 78q^{59} + 36q^{60} - 42q^{61} - 216q^{63} + 32q^{64} - 84q^{65} - 144q^{66} - 58q^{67} + 60q^{68} + 84q^{70} - 24q^{71} - 48q^{72} + 318q^{73} + 96q^{74} + 132q^{75} + 126q^{77} + 96q^{78} + 110q^{79} + 24q^{80} + 18q^{81} - 120q^{82} + 12q^{84} - 36q^{85} + 24q^{86} - 144q^{87} - 24q^{88} - 378q^{89} + 24q^{91} - 120q^{92} - 138q^{93} - 12q^{94} - 30q^{95} - 48q^{96} - 120q^{98} + 144q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(14))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
14.3.b $$\chi_{14}(13, \cdot)$$ None 0 1
14.3.d $$\chi_{14}(3, \cdot)$$ 14.3.d.a 4 2

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(14))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(14)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 2}$$