# Properties

 Label 76.4 Level 76 Weight 4 Dimension 297 Nonzero newspaces 6 Newform subspaces 7 Sturm bound 1440 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$6$$ Newform subspaces: $$7$$ Sturm bound: $$1440$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(76))$$.

Total New Old
Modular forms 585 333 252
Cusp forms 495 297 198
Eisenstein series 90 36 54

## Trace form

 $$297q - 9q^{2} - 9q^{4} - 18q^{5} - 9q^{6} - 9q^{8} - 18q^{9} + O(q^{10})$$ $$297q - 9q^{2} - 9q^{4} - 18q^{5} - 9q^{6} - 9q^{8} - 18q^{9} - 9q^{10} - 9q^{12} - 162q^{13} - 9q^{14} + 108q^{15} - 9q^{16} + 126q^{17} + 378q^{19} - 18q^{20} + 234q^{21} - 9q^{22} - 18q^{23} - 9q^{24} - 450q^{25} - 9q^{26} + 9q^{27} + 1422q^{28} + 612q^{29} + 1188q^{30} + 90q^{31} - 324q^{32} - 936q^{33} - 1134q^{34} - 1116q^{35} - 3159q^{36} - 666q^{37} - 2340q^{38} - 1890q^{39} - 1962q^{40} - 468q^{41} - 1539q^{42} - 630q^{43} + 216q^{44} - 1044q^{45} + 1566q^{46} + 36q^{47} + 4590q^{48} + 1692q^{49} + 3204q^{50} + 2475q^{51} - 9q^{52} + 1566q^{53} - 252q^{54} + 1944q^{55} + 2502q^{57} - 18q^{58} + 2250q^{59} - 2736q^{60} + 6948q^{61} - 4824q^{62} + 2448q^{63} - 4113q^{64} + 1152q^{65} - 1089q^{66} - 1242q^{67} + 1188q^{68} - 7470q^{69} + 4851q^{70} - 5148q^{71} + 8496q^{72} - 6255q^{73} + 5319q^{74} - 3150q^{75} + 6741q^{76} - 11142q^{77} + 6273q^{78} - 5274q^{79} + 3951q^{80} - 6831q^{81} + 4446q^{82} - 1368q^{83} + 315q^{84} + 2286q^{85} - 2214q^{86} + 4788q^{87} - 5841q^{88} + 7488q^{89} - 8604q^{90} + 6912q^{91} - 8874q^{92} + 16308q^{93} + 10782q^{95} + 13878q^{96} + 8082q^{97} + 12564q^{98} + 11439q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(76))$$

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
76.4.a $$\chi_{76}(1, \cdot)$$ 76.4.a.a 2 1
76.4.a.b 3
76.4.d $$\chi_{76}(75, \cdot)$$ 76.4.d.a 28 1
76.4.e $$\chi_{76}(45, \cdot)$$ 76.4.e.a 10 2
76.4.f $$\chi_{76}(27, \cdot)$$ 76.4.f.a 56 2
76.4.i $$\chi_{76}(5, \cdot)$$ 76.4.i.a 30 6
76.4.k $$\chi_{76}(3, \cdot)$$ 76.4.k.a 168 6

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(76))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(76)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 2}$$