## Defining parameters

 Level: $$N$$ = $$4 = 2^{2}$$ Weight: $$k$$ = $$7$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$7$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(\Gamma_1(4))$$.

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

## Trace form

 $$2q + 4q^{2} - 112q^{4} + 20q^{5} + 480q^{6} - 704q^{8} - 462q^{9} + O(q^{10})$$ $$2q + 4q^{2} - 112q^{4} + 20q^{5} + 480q^{6} - 704q^{8} - 462q^{9} + 40q^{10} + 1920q^{12} + 2932q^{13} - 4800q^{14} + 4352q^{16} - 9532q^{17} - 924q^{18} - 1120q^{20} + 19200q^{21} + 14880q^{22} - 23040q^{24} - 31050q^{25} + 5864q^{26} - 19200q^{28} + 50996q^{29} + 4800q^{30} + 62464q^{32} - 59520q^{33} - 19064q^{34} + 25872q^{36} + 3988q^{37} - 116640q^{38} - 7040q^{40} + 58724q^{41} + 38400q^{42} + 59520q^{44} - 4620q^{45} + 162240q^{46} - 215040q^{48} + 43298q^{49} - 62100q^{50} - 164192q^{52} - 385708q^{53} + 239040q^{54} + 230400q^{56} + 466560q^{57} + 101992q^{58} + 19200q^{60} - 21836q^{61} - 648960q^{62} - 28672q^{64} + 29320q^{65} - 119040q^{66} + 533792q^{68} - 648960q^{69} - 48000q^{70} + 162624q^{72} + 577252q^{73} + 7976q^{74} - 466560q^{76} + 595200q^{77} + 703680q^{78} + 43520q^{80} - 1292958q^{81} + 117448q^{82} - 1075200q^{84} - 95320q^{85} + 333600q^{86} - 714240q^{88} + 621476q^{89} - 9240q^{90} + 648960q^{92} + 2595840q^{93} + 117120q^{94} + 614400q^{96} - 2914172q^{97} + 86596q^{98} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(\Gamma_1(4))$$

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
4.7.b $$\chi_{4}(3, \cdot)$$ 4.7.b.a 2 1