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Properties

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

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Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 48 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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

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