Properties

Label 403.2
Level 403
Weight 2
Dimension 6305
Nonzero newspaces 30
Newforms 48
Sturm bound 26880
Trace bound 3

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Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newforms: \( 48 \)
Sturm bound: \(26880\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(403))\).

Total New Old
Modular forms 7080 6945 135
Cusp forms 6361 6305 56
Eisenstein series 719 640 79

Trace form

\( 6305q - 147q^{2} - 150q^{3} - 159q^{4} - 156q^{5} - 174q^{6} - 158q^{7} - 165q^{8} - 161q^{9} + O(q^{10}) \) \( 6305q - 147q^{2} - 150q^{3} - 159q^{4} - 156q^{5} - 174q^{6} - 158q^{7} - 165q^{8} - 161q^{9} - 162q^{10} - 162q^{11} - 170q^{12} - 156q^{13} - 354q^{14} - 186q^{15} - 191q^{16} - 174q^{17} - 189q^{18} - 158q^{19} - 198q^{20} - 172q^{21} - 126q^{22} - 156q^{23} - 78q^{24} - 119q^{25} - 144q^{26} - 264q^{27} - 46q^{28} - 114q^{29} - 60q^{30} - 121q^{31} - 165q^{32} - 138q^{33} - 84q^{34} - 138q^{35} - 83q^{36} - 128q^{37} - 174q^{38} - 162q^{39} - 312q^{40} - 144q^{41} - 186q^{42} - 168q^{43} - 234q^{44} - 222q^{45} - 186q^{46} - 198q^{47} - 204q^{48} - 133q^{49} - 81q^{50} - 18q^{51} - 101q^{52} - 312q^{53} + 36q^{54} - 102q^{55} - 50q^{57} - 48q^{58} - 174q^{59} + 192q^{60} - 69q^{62} - 164q^{63} - 33q^{64} - 63q^{65} - 24q^{66} - 170q^{67} - 60q^{68} - 90q^{69} - 24q^{70} - 114q^{71} - 21q^{72} - 164q^{73} - 84q^{74} - 56q^{75} - 28q^{76} - 96q^{77} + 6q^{78} - 356q^{79} - 6q^{80} - 173q^{81} - 174q^{82} - 24q^{83} - 14q^{84} - 156q^{85} - 42q^{86} - 138q^{87} + 30q^{88} - 66q^{89} + 54q^{90} - 108q^{91} - 132q^{92} - 22q^{93} - 312q^{94} - 42q^{95} + 48q^{96} - 142q^{97} - 3q^{98} - 156q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(403))\)

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
403.2.a \(\chi_{403}(1, \cdot)\) 403.2.a.a 2 1
403.2.a.b 6
403.2.a.c 7
403.2.a.d 8
403.2.a.e 8
403.2.c \(\chi_{403}(311, \cdot)\) 403.2.c.a 2 1
403.2.c.b 32
403.2.e \(\chi_{403}(191, \cdot)\) 403.2.e.a 70 2
403.2.f \(\chi_{403}(94, \cdot)\) 403.2.f.a 2 2
403.2.f.b 34
403.2.f.c 36
403.2.g \(\chi_{403}(87, \cdot)\) 403.2.g.a 70 2
403.2.h \(\chi_{403}(118, \cdot)\) 403.2.h.a 30 2
403.2.h.b 34
403.2.i \(\chi_{403}(216, \cdot)\) 403.2.i.a 68 2
403.2.k \(\chi_{403}(66, \cdot)\) 403.2.k.a 4 4
403.2.k.b 4
403.2.k.c 4
403.2.k.d 48
403.2.k.e 68
403.2.l \(\chi_{403}(25, \cdot)\) 403.2.l.a 2 2
403.2.l.b 2
403.2.l.c 68
403.2.r \(\chi_{403}(218, \cdot)\) 403.2.r.a 68 2
403.2.s \(\chi_{403}(160, \cdot)\) 403.2.s.a 70 2
403.2.v \(\chi_{403}(36, \cdot)\) 403.2.v.a 70 2
403.2.y \(\chi_{403}(64, \cdot)\) 403.2.y.a 136 4
403.2.ba \(\chi_{403}(6, \cdot)\) 403.2.ba.a 140 4
403.2.be \(\chi_{403}(57, \cdot)\) 403.2.be.a 4 4
403.2.be.b 4
403.2.be.c 136
403.2.bf \(\chi_{403}(37, \cdot)\) 403.2.bf.a 140 4
403.2.bg \(\chi_{403}(123, \cdot)\) 403.2.bg.a 144 4
403.2.bi \(\chi_{403}(14, \cdot)\) 403.2.bi.a 120 8
403.2.bi.b 136
403.2.bj \(\chi_{403}(100, \cdot)\) 403.2.bj.a 280 8
403.2.bk \(\chi_{403}(9, \cdot)\) 403.2.bk.a 280 8
403.2.bl \(\chi_{403}(16, \cdot)\) 403.2.bl.a 8 8
403.2.bl.b 280
403.2.bn \(\chi_{403}(60, \cdot)\) 403.2.bn.a 272 8
403.2.bp \(\chi_{403}(10, \cdot)\) 403.2.bp.a 280 8
403.2.bs \(\chi_{403}(4, \cdot)\) 403.2.bs.a 288 8
403.2.bt \(\chi_{403}(82, \cdot)\) 403.2.bt.a 280 8
403.2.bz \(\chi_{403}(38, \cdot)\) 403.2.bz.a 288 8
403.2.cb \(\chi_{403}(15, \cdot)\) 403.2.cb.a 576 16
403.2.cc \(\chi_{403}(24, \cdot)\) 403.2.cc.a 560 16
403.2.cd \(\chi_{403}(21, \cdot)\) 403.2.cd.a 576 16
403.2.ch \(\chi_{403}(11, \cdot)\) 403.2.ch.a 560 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(403))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(403)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)