# Properties

 Label 380.2 Level 380 Weight 2 Dimension 2196 Nonzero newspaces 18 Newform subspaces 36 Sturm bound 17280 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Newform subspaces: $$36$$ Sturm bound: $$17280$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(380))$$.

Total New Old
Modular forms 4680 2396 2284
Cusp forms 3961 2196 1765
Eisenstein series 719 200 519

## Trace form

 $$2196 q - 14 q^{2} + 4 q^{3} - 18 q^{4} - 44 q^{5} - 54 q^{6} - 4 q^{7} - 26 q^{8} - 38 q^{9} + O(q^{10})$$ $$2196 q - 14 q^{2} + 4 q^{3} - 18 q^{4} - 44 q^{5} - 54 q^{6} - 4 q^{7} - 26 q^{8} - 38 q^{9} - 39 q^{10} - 18 q^{12} - 12 q^{13} - 18 q^{14} + 14 q^{15} - 38 q^{16} - 18 q^{17} - 24 q^{18} + 46 q^{19} - 46 q^{20} - 58 q^{21} - 18 q^{22} + 6 q^{23} - 18 q^{24} - 50 q^{25} - 62 q^{26} - 2 q^{27} - 72 q^{28} - 84 q^{29} - 90 q^{30} - 28 q^{31} - 124 q^{32} - 144 q^{33} - 108 q^{34} - 32 q^{35} - 258 q^{36} - 84 q^{37} - 144 q^{38} - 100 q^{39} - 82 q^{40} - 124 q^{41} - 198 q^{42} - 46 q^{43} - 108 q^{44} - 91 q^{45} - 144 q^{46} + 30 q^{47} - 144 q^{48} - 24 q^{49} - 26 q^{50} + 48 q^{51} - 10 q^{52} + 12 q^{53} + 36 q^{54} + 36 q^{55} - 72 q^{56} + 46 q^{57} - 52 q^{58} + 66 q^{59} - 36 q^{60} - 172 q^{61} + 72 q^{62} + 20 q^{63} + 126 q^{64} - 63 q^{65} + 90 q^{66} - 34 q^{67} + 132 q^{68} - 246 q^{69} + 81 q^{70} + 42 q^{71} + 276 q^{72} - 152 q^{73} + 90 q^{74} - 8 q^{75} + 126 q^{76} - 342 q^{77} + 126 q^{78} - 136 q^{79} + 13 q^{80} - 284 q^{81} + 220 q^{82} - 102 q^{83} + 198 q^{84} - 282 q^{85} + 72 q^{86} - 192 q^{87} + 126 q^{88} - 186 q^{89} - 12 q^{90} - 128 q^{91} + 72 q^{92} - 280 q^{93} - 121 q^{95} - 252 q^{96} - 218 q^{97} - 244 q^{98} - 270 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$

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
380.2.a $$\chi_{380}(1, \cdot)$$ 380.2.a.a 1 1
380.2.a.b 1
380.2.a.c 2
380.2.a.d 2
380.2.c $$\chi_{380}(229, \cdot)$$ 380.2.c.a 4 1
380.2.c.b 6
380.2.d $$\chi_{380}(379, \cdot)$$ 380.2.d.a 16 1
380.2.d.b 40
380.2.f $$\chi_{380}(151, \cdot)$$ 380.2.f.a 20 1
380.2.f.b 20
380.2.i $$\chi_{380}(121, \cdot)$$ 380.2.i.a 2 2
380.2.i.b 6
380.2.i.c 8
380.2.k $$\chi_{380}(267, \cdot)$$ 380.2.k.a 2 2
380.2.k.b 2
380.2.k.c 52
380.2.k.d 52
380.2.l $$\chi_{380}(37, \cdot)$$ 380.2.l.a 8 2
380.2.l.b 12
380.2.n $$\chi_{380}(31, \cdot)$$ 380.2.n.a 40 2
380.2.n.b 40
380.2.r $$\chi_{380}(49, \cdot)$$ 380.2.r.a 20 2
380.2.s $$\chi_{380}(179, \cdot)$$ 380.2.s.a 112 2
380.2.u $$\chi_{380}(61, \cdot)$$ 380.2.u.a 18 6
380.2.u.b 18
380.2.v $$\chi_{380}(7, \cdot)$$ 380.2.v.a 4 4
380.2.v.b 4
380.2.v.c 216
380.2.y $$\chi_{380}(217, \cdot)$$ 380.2.y.a 4 4
380.2.y.b 36
380.2.bb $$\chi_{380}(59, \cdot)$$ 380.2.bb.a 336 6
380.2.bd $$\chi_{380}(9, \cdot)$$ 380.2.bd.a 60 6
380.2.be $$\chi_{380}(51, \cdot)$$ 380.2.be.a 120 6
380.2.be.b 120
380.2.bh $$\chi_{380}(13, \cdot)$$ 380.2.bh.a 120 12
380.2.bj $$\chi_{380}(23, \cdot)$$ 380.2.bj.a 672 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(380))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(380)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 2}$$