## Defining parameters

 Level: $$N$$ = $$14 = 2 \cdot 7$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$2$$ Newform subspaces: $$4$$ Sturm bound: $$48$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(14))$$.

Total New Old
Modular forms 24 6 18
Cusp forms 12 6 6
Eisenstein series 12 0 12

## Trace form

 $$6q + 12q^{3} - 24q^{5} - 36q^{6} - 48q^{7} + 42q^{9} + O(q^{10})$$ $$6q + 12q^{3} - 24q^{5} - 36q^{6} - 48q^{7} + 42q^{9} + 36q^{10} + 42q^{11} + 48q^{12} + 66q^{13} + 132q^{14} - 12q^{15} - 150q^{17} - 168q^{18} - 60q^{19} - 120q^{20} - 72q^{21} - 216q^{22} - 294q^{23} - 48q^{24} + 210q^{25} + 348q^{26} + 576q^{27} + 120q^{28} + 576q^{29} + 168q^{30} + 210q^{31} - 570q^{33} - 408q^{34} - 420q^{35} - 168q^{36} + 42q^{37} + 108q^{38} - 252q^{39} + 144q^{40} - 792q^{41} + 324q^{42} - 516q^{43} + 168q^{44} - 78q^{45} - 168q^{46} - 18q^{47} - 96q^{48} - 90q^{49} + 24q^{50} + 1134q^{51} + 312q^{52} + 1302q^{53} - 144q^{54} + 1332q^{55} + 48q^{56} + 312q^{57} - 504q^{58} - 264q^{59} - 504q^{60} + 840q^{61} + 120q^{62} - 48q^{63} + 384q^{64} - 2016q^{65} - 384q^{66} - 2058q^{67} - 600q^{68} - 1332q^{69} - 756q^{70} - 792q^{71} - 672q^{72} - 594q^{73} + 1512q^{74} + 234q^{75} + 1464q^{76} + 2226q^{77} + 1152q^{78} + 1050q^{79} - 384q^{80} + 84q^{81} - 984q^{82} - 6q^{83} - 912q^{84} + 240q^{85} + 840q^{86} + 2304q^{87} + 1344q^{88} + 2310q^{89} + 2388q^{90} + 906q^{91} - 432q^{92} + 294q^{93} - 816q^{94} - 2058q^{95} - 192q^{96} - 4224q^{97} - 2640q^{98} - 3732q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(14))$$

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
14.4.a $$\chi_{14}(1, \cdot)$$ 14.4.a.a 1 1
14.4.a.b 1
14.4.c $$\chi_{14}(9, \cdot)$$ 14.4.c.a 2 2
14.4.c.b 2

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(14))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(14)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 2}$$