↑

Properties

Label 403.3
Level 403
Weight 3
Dimension 12934
Nonzero newspaces 30
Newform subspaces 32
Sturm bound 40320
Trace bound 6

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 32 \)
Sturm bound: \(40320\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(403))\).

Total New Old
Modular forms 13800 13570 230
Cusp forms 13080 12934 146
Eisenstein series 720 636 84

Trace form

\( 12934 q - 138 q^{2} - 138 q^{3} - 138 q^{4} - 138 q^{5} - 138 q^{6} - 158 q^{7} - 210 q^{8} - 186 q^{9} + O(q^{10}) \) \( 12934 q - 138 q^{2} - 138 q^{3} - 138 q^{4} - 138 q^{5} - 138 q^{6} - 158 q^{7} - 210 q^{8} - 186 q^{9} - 198 q^{10} - 150 q^{11} - 150 q^{12} - 129 q^{13} - 258 q^{14} - 66 q^{15} + 22 q^{16} - 126 q^{17} - 210 q^{18} - 170 q^{19} - 234 q^{20} - 384 q^{21} - 798 q^{22} - 396 q^{23} - 1002 q^{24} - 500 q^{25} - 213 q^{26} - 432 q^{27} - 390 q^{28} - 294 q^{29} - 72 q^{30} - 110 q^{31} + 60 q^{32} + 246 q^{33} + 582 q^{34} + 222 q^{35} + 918 q^{36} + 536 q^{37} + 330 q^{38} + 18 q^{39} + 558 q^{40} - 84 q^{41} + 330 q^{42} - 380 q^{43} + 18 q^{44} - 258 q^{45} - 354 q^{46} - 6 q^{47} - 1068 q^{48} - 726 q^{49} - 1452 q^{50} - 1950 q^{51} - 1000 q^{52} - 906 q^{53} - 2796 q^{54} - 798 q^{55} - 1332 q^{56} - 750 q^{57} - 420 q^{58} - 54 q^{59} - 504 q^{60} + 660 q^{61} + 24 q^{62} + 204 q^{63} + 510 q^{64} - 21 q^{65} + 1536 q^{66} + 142 q^{67} + 288 q^{68} + 1146 q^{69} + 2016 q^{70} + 654 q^{71} + 3432 q^{72} + 454 q^{73} + 1464 q^{74} + 1764 q^{75} + 312 q^{76} - 540 q^{77} + 12 q^{78} - 1288 q^{79} - 3294 q^{80} - 1026 q^{81} - 1398 q^{82} - 1560 q^{83} - 2670 q^{84} - 894 q^{85} - 1182 q^{86} - 1146 q^{87} - 1182 q^{88} - 780 q^{89} - 1140 q^{90} - 646 q^{91} + 864 q^{92} + 30 q^{93} + 792 q^{94} + 726 q^{95} + 840 q^{96} + 280 q^{97} + 1590 q^{98} + 180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(403))\)

We only show spaces with odd 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
403.3.b \(\chi_{403}(402, \cdot)\) 403.3.b.a 1 1
403.3.b.b 1
403.3.b.c 72
403.3.d \(\chi_{403}(92, \cdot)\) 403.3.d.a 64 1
403.3.j \(\chi_{403}(125, \cdot)\) 403.3.j.a 140 2
403.3.m \(\chi_{403}(181, \cdot)\) 403.3.m.a 144 2
403.3.n \(\chi_{403}(347, \cdot)\) 403.3.n.a 146 2
403.3.o \(\chi_{403}(68, \cdot)\) 403.3.o.a 146 2
403.3.p \(\chi_{403}(61, \cdot)\) 403.3.p.a 144 2
403.3.q \(\chi_{403}(88, \cdot)\) 403.3.q.a 146 2
403.3.t \(\chi_{403}(30, \cdot)\) 403.3.t.a 144 2
403.3.u \(\chi_{403}(192, \cdot)\) 403.3.u.a 146 2
403.3.w \(\chi_{403}(274, \cdot)\) 403.3.w.a 128 2
403.3.x \(\chi_{403}(27, \cdot)\) 403.3.x.a 256 4
403.3.z \(\chi_{403}(77, \cdot)\) 403.3.z.a 296 4
403.3.bb \(\chi_{403}(5, \cdot)\) 403.3.bb.a 288 4
403.3.bc \(\chi_{403}(98, \cdot)\) 403.3.bc.a 292 4
403.3.bd \(\chi_{403}(32, \cdot)\) 403.3.bd.a 280 4
403.3.bh \(\chi_{403}(67, \cdot)\) 403.3.bh.a 292 4
403.3.bm \(\chi_{403}(8, \cdot)\) 403.3.bm.a 592 8
403.3.bo \(\chi_{403}(53, \cdot)\) 403.3.bo.a 512 8
403.3.bq \(\chi_{403}(23, \cdot)\) 403.3.bq.a 576 8
403.3.br \(\chi_{403}(127, \cdot)\) 403.3.br.a 584 8
403.3.bu \(\chi_{403}(17, \cdot)\) 403.3.bu.a 584 8
403.3.bv \(\chi_{403}(3, \cdot)\) 403.3.bv.a 584 8
403.3.bw \(\chi_{403}(29, \cdot)\) 403.3.bw.a 576 8
403.3.bx \(\chi_{403}(42, \cdot)\) 403.3.bx.a 584 8
403.3.by \(\chi_{403}(12, \cdot)\) 403.3.by.a 576 8
403.3.ca \(\chi_{403}(7, \cdot)\) 403.3.ca.a 1168 16
403.3.ce \(\chi_{403}(2, \cdot)\) 403.3.ce.a 1152 16
403.3.cf \(\chi_{403}(20, \cdot)\) 403.3.cf.a 1168 16
403.3.cg \(\chi_{403}(18, \cdot)\) 403.3.cg.a 1152 16

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(403))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(403)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)