# Properties

 Label 363.2 Level 363 Weight 2 Dimension 3431 Nonzero newspaces 8 Newform subspaces 45 Sturm bound 19360 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$363 = 3 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$45$$ Sturm bound: $$19360$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(363))$$.

Total New Old
Modular forms 5160 3711 1449
Cusp forms 4521 3431 1090
Eisenstein series 639 280 359

## Trace form

 $$3431q + 3q^{2} - 44q^{3} - 83q^{4} + 6q^{5} - 52q^{6} - 102q^{7} - 25q^{8} - 64q^{9} + O(q^{10})$$ $$3431q + 3q^{2} - 44q^{3} - 83q^{4} + 6q^{5} - 52q^{6} - 102q^{7} - 25q^{8} - 64q^{9} - 132q^{10} - 10q^{11} - 118q^{12} - 96q^{13} - 36q^{14} - 79q^{15} - 179q^{16} - 42q^{17} - 72q^{18} - 130q^{19} - 58q^{20} - 87q^{21} - 160q^{22} - 16q^{23} - 80q^{24} - 139q^{25} - 58q^{26} - 14q^{27} - 134q^{28} - 10q^{29} - 37q^{30} - 98q^{31} + 23q^{32} - 40q^{33} - 196q^{34} - 32q^{35} - 48q^{36} - 132q^{37} - 40q^{38} - 81q^{39} - 220q^{40} - 78q^{41} - 91q^{42} - 186q^{43} - 110q^{44} - 169q^{45} - 278q^{46} - 92q^{47} - 164q^{48} - 253q^{49} - 127q^{50} - 137q^{51} - 252q^{52} - 86q^{53} - 72q^{54} - 180q^{55} - 120q^{56} - 15q^{57} - 180q^{58} - 53q^{60} - 128q^{61} - 24q^{62} - 7q^{63} - 163q^{64} - 36q^{65} - 45q^{66} - 202q^{67} - 74q^{68} - 41q^{69} - 246q^{70} - 48q^{71} - 20q^{72} - 196q^{73} - 66q^{74} - 104q^{75} - 330q^{76} - 90q^{77} - 143q^{78} - 270q^{79} - 234q^{80} - 64q^{81} - 184q^{82} - 176q^{83} - 119q^{84} - 242q^{85} - 148q^{86} - 145q^{87} - 260q^{88} - 70q^{89} - 157q^{90} - 198q^{91} - 172q^{92} - 173q^{93} - 246q^{94} - 180q^{95} - 112q^{96} - 232q^{97} - 269q^{98} - 80q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(363))$$

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
363.2.a $$\chi_{363}(1, \cdot)$$ 363.2.a.a 1 1
363.2.a.b 1
363.2.a.c 1
363.2.a.d 2
363.2.a.e 2
363.2.a.f 2
363.2.a.g 2
363.2.a.h 2
363.2.a.i 2
363.2.a.j 4
363.2.d $$\chi_{363}(362, \cdot)$$ 363.2.d.a 2 1
363.2.d.b 2
363.2.d.c 4
363.2.d.d 4
363.2.d.e 8
363.2.d.f 8
363.2.e $$\chi_{363}(124, \cdot)$$ 363.2.e.a 4 4
363.2.e.b 4
363.2.e.c 4
363.2.e.d 4
363.2.e.e 4
363.2.e.f 4
363.2.e.g 4
363.2.e.h 4
363.2.e.i 4
363.2.e.j 4
363.2.e.k 4
363.2.e.l 4
363.2.e.m 8
363.2.e.n 16
363.2.f $$\chi_{363}(161, \cdot)$$ 363.2.f.a 8 4
363.2.f.b 8
363.2.f.c 8
363.2.f.d 8
363.2.f.e 8
363.2.f.f 8
363.2.f.g 16
363.2.f.h 16
363.2.f.i 32
363.2.i $$\chi_{363}(34, \cdot)$$ 363.2.i.a 110 10
363.2.i.b 110
363.2.j $$\chi_{363}(32, \cdot)$$ 363.2.j.a 420 10
363.2.m $$\chi_{363}(4, \cdot)$$ 363.2.m.a 440 40
363.2.m.b 440
363.2.p $$\chi_{363}(2, \cdot)$$ 363.2.p.a 1680 40

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(363))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(363)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 2}$$