# Properties

 Label 402.2 Level 402 Weight 2 Dimension 1123 Nonzero newspaces 8 Newforms 27 Sturm bound 17952 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$402 = 2 \cdot 3 \cdot 67$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newforms: $$27$$ Sturm bound: $$17952$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(402))$$.

Total New Old
Modular forms 4752 1123 3629
Cusp forms 4225 1123 3102
Eisenstein series 527 0 527

## Trace form

 $$1123q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + O(q^{10})$$ $$1123q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + 6q^{10} + 12q^{11} + q^{12} + 14q^{13} + 8q^{14} + 6q^{15} + q^{16} + 18q^{17} + q^{18} + 20q^{19} + 6q^{20} + 8q^{21} + 12q^{22} + 24q^{23} + q^{24} + 31q^{25} + 14q^{26} + q^{27} + 8q^{28} + 30q^{29} + 6q^{30} + 32q^{31} + q^{32} + 12q^{33} + 18q^{34} + 48q^{35} + q^{36} + 38q^{37} + 20q^{38} + 14q^{39} + 6q^{40} + 42q^{41} + 8q^{42} + 44q^{43} + 12q^{44} + 6q^{45} + 24q^{46} + 48q^{47} + q^{48} + 57q^{49} + 31q^{50} + 18q^{51} - 30q^{52} - 78q^{53} + q^{54} - 324q^{55} + 8q^{56} - 134q^{57} - 234q^{58} - 204q^{59} - 126q^{60} - 466q^{61} - 100q^{62} - 14q^{63} + q^{64} - 444q^{65} - 252q^{66} - 197q^{67} - 114q^{68} - 108q^{69} - 480q^{70} - 456q^{71} + q^{72} - 498q^{73} - 94q^{74} - 233q^{75} - 244q^{76} - 168q^{77} - 118q^{78} - 228q^{79} + 6q^{80} + q^{81} - 156q^{82} - 48q^{83} - 14q^{84} + 108q^{85} + 44q^{86} + 30q^{87} + 12q^{88} + 90q^{89} + 6q^{90} + 112q^{91} + 24q^{92} + 32q^{93} + 48q^{94} + 120q^{95} + q^{96} + 98q^{97} + 57q^{98} + 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(402))$$

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
402.2.a $$\chi_{402}(1, \cdot)$$ 402.2.a.a 1 1
402.2.a.b 1
402.2.a.c 1
402.2.a.d 1
402.2.a.e 2
402.2.a.f 2
402.2.a.g 3
402.2.d $$\chi_{402}(401, \cdot)$$ 402.2.d.a 12 1
402.2.d.b 12
402.2.e $$\chi_{402}(37, \cdot)$$ 402.2.e.a 6 2
402.2.e.b 6
402.2.e.c 6
402.2.e.d 6
402.2.h $$\chi_{402}(239, \cdot)$$ 402.2.h.a 22 2
402.2.h.b 22
402.2.i $$\chi_{402}(25, \cdot)$$ 402.2.i.a 20 10
402.2.i.b 20
402.2.i.c 30
402.2.i.d 30
402.2.j $$\chi_{402}(5, \cdot)$$ 402.2.j.a 120 10
402.2.j.b 120
402.2.m $$\chi_{402}(19, \cdot)$$ 402.2.m.a 60 20
402.2.m.b 60
402.2.m.c 60
402.2.m.d 60
402.2.n $$\chi_{402}(11, \cdot)$$ 402.2.n.a 220 20
402.2.n.b 220

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(402))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(402)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(67))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(134))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(201))$$$$^{\oplus 2}$$