Properties

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

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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

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

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

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