# Properties

 Label 14.3 Level 14 Weight 3 Dimension 4 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 36 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$14 = 2 \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ 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

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

## 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

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