Properties

Label 465.2
Level 465
Weight 2
Dimension 5099
Nonzero newspaces 24
Newform subspaces 61
Sturm bound 30720
Trace bound 4

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Defining parameters

Level: \( N \) = \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 61 \)
Sturm bound: \(30720\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(465))\).

Total New Old
Modular forms 8160 5443 2717
Cusp forms 7201 5099 2102
Eisenstein series 959 344 615

Trace form

\( 5099q + 5q^{2} - 27q^{3} - 51q^{4} - q^{5} - 89q^{6} - 52q^{7} + 9q^{8} - 31q^{9} + O(q^{10}) \) \( 5099q + 5q^{2} - 27q^{3} - 51q^{4} - q^{5} - 89q^{6} - 52q^{7} + 9q^{8} - 31q^{9} - 85q^{10} + 20q^{11} - 25q^{12} - 42q^{13} + 24q^{14} - 42q^{15} - 147q^{16} + 14q^{17} - 25q^{18} - 48q^{19} + 9q^{20} - 92q^{21} - 152q^{22} - 36q^{23} - 129q^{24} - 111q^{25} - 82q^{26} - 27q^{27} - 324q^{28} - 86q^{29} - 119q^{30} - 269q^{31} - 287q^{32} - 86q^{33} - 242q^{34} - 52q^{35} - 121q^{36} - 182q^{37} - 52q^{38} - 90q^{39} - 201q^{40} - 38q^{41} - 66q^{42} - 44q^{43} + 76q^{44} - 46q^{45} - 108q^{46} + 32q^{47} - 91q^{48} - 109q^{49} - 145q^{50} - 248q^{51} - 266q^{52} - 46q^{53} - 359q^{54} - 190q^{55} - 420q^{56} - 182q^{57} - 394q^{58} - 52q^{59} - 235q^{60} - 534q^{61} - 267q^{62} - 292q^{63} - 427q^{64} - 162q^{65} - 496q^{66} - 136q^{67} - 290q^{68} - 186q^{69} - 336q^{70} - 152q^{71} - 351q^{72} - 126q^{73} - 206q^{74} - 117q^{75} - 332q^{76} - 24q^{77} + 106q^{78} + 20q^{79} + 33q^{80} + 29q^{81} + 86q^{82} + 60q^{83} + 386q^{84} - 76q^{85} + 140q^{86} + 116q^{87} + 144q^{88} + 102q^{89} + 140q^{90} - 68q^{91} + 168q^{92} + 241q^{93} + 40q^{94} + 12q^{95} + 233q^{96} + 34q^{97} + 157q^{98} + 140q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)

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
465.2.a \(\chi_{465}(1, \cdot)\) 465.2.a.a 1 1
465.2.a.b 1
465.2.a.c 2
465.2.a.d 2
465.2.a.e 3
465.2.a.f 3
465.2.a.g 3
465.2.a.h 4
465.2.c \(\chi_{465}(94, \cdot)\) 465.2.c.a 10 1
465.2.c.b 22
465.2.e \(\chi_{465}(371, \cdot)\) 465.2.e.a 44 1
465.2.g \(\chi_{465}(464, \cdot)\) 465.2.g.a 4 1
465.2.g.b 4
465.2.g.c 4
465.2.g.d 8
465.2.g.e 8
465.2.g.f 32
465.2.i \(\chi_{465}(211, \cdot)\) 465.2.i.a 2 2
465.2.i.b 4
465.2.i.c 6
465.2.i.d 8
465.2.i.e 10
465.2.i.f 14
465.2.j \(\chi_{465}(247, \cdot)\) 465.2.j.a 64 2
465.2.k \(\chi_{465}(32, \cdot)\) 465.2.k.a 60 2
465.2.k.b 60
465.2.n \(\chi_{465}(16, \cdot)\) 465.2.n.a 4 4
465.2.n.b 4
465.2.n.c 8
465.2.n.d 16
465.2.n.e 20
465.2.n.f 28
465.2.o \(\chi_{465}(26, \cdot)\) 465.2.o.a 84 2
465.2.q \(\chi_{465}(304, \cdot)\) 465.2.q.a 4 2
465.2.q.b 60
465.2.t \(\chi_{465}(119, \cdot)\) 465.2.t.a 4 2
465.2.t.b 4
465.2.t.c 8
465.2.t.d 104
465.2.w \(\chi_{465}(29, \cdot)\) 465.2.w.a 8 4
465.2.w.b 8
465.2.w.c 224
465.2.y \(\chi_{465}(116, \cdot)\) 465.2.y.a 176 4
465.2.ba \(\chi_{465}(4, \cdot)\) 465.2.ba.a 128 4
465.2.be \(\chi_{465}(98, \cdot)\) 465.2.be.a 240 4
465.2.bf \(\chi_{465}(37, \cdot)\) 465.2.bf.a 128 4
465.2.bg \(\chi_{465}(76, \cdot)\) 465.2.bg.a 32 8
465.2.bg.b 40
465.2.bg.c 48
465.2.bg.d 56
465.2.bj \(\chi_{465}(2, \cdot)\) 465.2.bj.a 480 8
465.2.bk \(\chi_{465}(58, \cdot)\) 465.2.bk.a 256 8
465.2.bm \(\chi_{465}(44, \cdot)\) 465.2.bm.a 8 8
465.2.bm.b 8
465.2.bm.c 8
465.2.bm.d 8
465.2.bm.e 448
465.2.bp \(\chi_{465}(19, \cdot)\) 465.2.bp.a 256 8
465.2.br \(\chi_{465}(11, \cdot)\) 465.2.br.a 336 8
465.2.bs \(\chi_{465}(13, \cdot)\) 465.2.bs.a 512 16
465.2.bt \(\chi_{465}(38, \cdot)\) 465.2.bt.a 960 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(465))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(465)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 2}\)