## Defining parameters

 Level: $$N$$ = $$7$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$16$$ Trace bound: $$1$$

## Dimensions

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

Total New Old
Modular forms 9 7 2
Cusp forms 3 3 0
Eisenstein series 6 4 2

## Trace form

 $$3q - 3q^{2} - 9q^{3} - 3q^{4} + 9q^{5} + 30q^{6} + 21q^{7} - 33q^{8} - 45q^{9} + O(q^{10})$$ $$3q - 3q^{2} - 9q^{3} - 3q^{4} + 9q^{5} + 30q^{6} + 21q^{7} - 33q^{8} - 45q^{9} - 30q^{10} - 3q^{11} + 42q^{12} + 21q^{14} + 66q^{15} + 57q^{16} + 75q^{17} - 21q^{18} - 159q^{19} - 168q^{20} - 231q^{21} - 12q^{22} + 207q^{23} + 138q^{24} + 207q^{25} + 30q^{27} + 189q^{28} + 6q^{29} - 66q^{30} - 135q^{31} - 321q^{32} + 51q^{33} - 138q^{34} - 63q^{35} - 15q^{36} - 465q^{37} + 12q^{38} + 42q^{39} + 408q^{40} + 882q^{41} + 378q^{42} - 120q^{43} + 36q^{44} - 522q^{45} + 270q^{46} - 201q^{47} - 306q^{48} + 147q^{49} - 435q^{50} + 39q^{51} - 252q^{52} - 465q^{53} - 30q^{54} - 198q^{55} - 777q^{56} + 906q^{57} - 6q^{58} + 915q^{59} + 420q^{60} - 75q^{61} + 576q^{62} + 315q^{63} + 729q^{64} + 546q^{65} + 54q^{66} - 171q^{67} - 462q^{68} - 2322q^{69} - 378q^{70} - 1632q^{71} + 183q^{72} + 411q^{73} - 192q^{74} + 270q^{75} + 378q^{76} + 231q^{77} - 336q^{78} + 543q^{79} + 768q^{80} + 1260q^{81} - 882q^{82} + 882q^{83} - 294q^{84} + 570q^{85} + 120q^{86} - 186q^{87} - 240q^{88} + 1059q^{89} + 984q^{90} - 588q^{91} + 936q^{92} - 1053q^{93} - 1374q^{94} - 2103q^{95} - 798q^{96} - 1470q^{97} + 1029q^{98} - 36q^{99} + O(q^{100})$$

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

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
7.4.a $$\chi_{7}(1, \cdot)$$ 7.4.a.a 1 1
7.4.c $$\chi_{7}(2, \cdot)$$ 7.4.c.a 2 2