## 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

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

## 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