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

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

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

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