## Defining parameters

 Level: $$N$$ = $$14 = 2 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(14))$$.

Total New Old
Modular forms 12 1 11
Cusp forms 1 1 0
Eisenstein series 11 0 11

## Trace form

 $$q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} + q^{7} - q^{8} + q^{9} + O(q^{10})$$ $$q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} + q^{7} - q^{8} + q^{9} - 2 q^{12} - 4 q^{13} - q^{14} + q^{16} + 6 q^{17} - q^{18} + 2 q^{19} - 2 q^{21} + 2 q^{24} - 5 q^{25} + 4 q^{26} + 4 q^{27} + q^{28} - 6 q^{29} - 4 q^{31} - q^{32} - 6 q^{34} + q^{36} + 2 q^{37} - 2 q^{38} + 8 q^{39} + 6 q^{41} + 2 q^{42} + 8 q^{43} - 12 q^{47} - 2 q^{48} + q^{49} + 5 q^{50} - 12 q^{51} - 4 q^{52} + 6 q^{53} - 4 q^{54} - q^{56} - 4 q^{57} + 6 q^{58} - 6 q^{59} + 8 q^{61} + 4 q^{62} + q^{63} + q^{64} - 4 q^{67} + 6 q^{68} - q^{72} + 2 q^{73} - 2 q^{74} + 10 q^{75} + 2 q^{76} - 8 q^{78} + 8 q^{79} - 11 q^{81} - 6 q^{82} - 6 q^{83} - 2 q^{84} - 8 q^{86} + 12 q^{87} - 6 q^{89} - 4 q^{91} + 8 q^{93} + 12 q^{94} + 2 q^{96} - 10 q^{97} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$

We only show spaces with even 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
14.2.a $$\chi_{14}(1, \cdot)$$ 14.2.a.a 1 1
14.2.c $$\chi_{14}(9, \cdot)$$ None 0 2