Properties

Label 315.3
Level 315
Weight 3
Dimension 4670
Nonzero newspaces 30
Newform subspaces 50
Sturm bound 20736
Trace bound 9

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 50 \)
Sturm bound: \(20736\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(315))\).

Total New Old
Modular forms 7296 4938 2358
Cusp forms 6528 4670 1858
Eisenstein series 768 268 500

Trace form

\( 4670 q - 22 q^{2} - 20 q^{3} - 30 q^{4} - 10 q^{5} - 4 q^{6} - 10 q^{7} + 30 q^{8} - 4 q^{9} + O(q^{10}) \) \( 4670 q - 22 q^{2} - 20 q^{3} - 30 q^{4} - 10 q^{5} - 4 q^{6} - 10 q^{7} + 30 q^{8} - 4 q^{9} + 52 q^{10} + 52 q^{11} + 128 q^{12} + 88 q^{13} + 246 q^{14} - 20 q^{15} + 214 q^{16} + 56 q^{17} - 8 q^{18} - 44 q^{19} - 150 q^{20} - 96 q^{21} - 64 q^{22} - 220 q^{23} - 324 q^{24} + 176 q^{25} + 52 q^{26} + 52 q^{27} - 222 q^{28} + 84 q^{29} - 34 q^{30} + 164 q^{31} + 170 q^{32} + 44 q^{33} + 416 q^{34} - 26 q^{35} - 764 q^{36} - 124 q^{37} - 852 q^{38} - 680 q^{39} - 738 q^{40} - 752 q^{41} - 384 q^{42} - 288 q^{43} - 1332 q^{44} - 40 q^{45} - 876 q^{46} - 484 q^{47} - 364 q^{48} - 38 q^{49} + 782 q^{50} - 268 q^{51} + 144 q^{52} - 376 q^{53} - 736 q^{54} + 76 q^{55} - 546 q^{56} + 172 q^{57} + 916 q^{58} + 1008 q^{59} + 590 q^{60} + 976 q^{61} + 1096 q^{62} + 252 q^{63} + 118 q^{64} + 308 q^{65} + 964 q^{66} + 12 q^{67} + 1840 q^{68} + 1320 q^{69} + 150 q^{70} + 1252 q^{71} + 2544 q^{72} + 316 q^{73} + 888 q^{74} - 812 q^{75} - 216 q^{76} + 632 q^{77} - 376 q^{78} + 96 q^{79} - 3094 q^{80} - 1612 q^{81} - 1388 q^{82} - 2488 q^{83} - 1836 q^{84} - 1472 q^{85} - 5228 q^{86} - 2492 q^{87} - 3864 q^{88} - 2940 q^{89} - 2294 q^{90} - 2776 q^{91} - 2884 q^{92} - 444 q^{93} - 3328 q^{94} - 1314 q^{95} - 1184 q^{96} - 2748 q^{97} - 3258 q^{98} + 520 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(315))\)

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
315.3.c \(\chi_{315}(71, \cdot)\) 315.3.c.a 16 1
315.3.e \(\chi_{315}(244, \cdot)\) 315.3.e.a 1 1
315.3.e.b 1
315.3.e.c 4
315.3.e.d 16
315.3.e.e 16
315.3.f \(\chi_{315}(134, \cdot)\) 315.3.f.a 24 1
315.3.h \(\chi_{315}(181, \cdot)\) 315.3.h.a 2 1
315.3.h.b 2
315.3.h.c 12
315.3.h.d 12
315.3.n \(\chi_{315}(62, \cdot)\) 315.3.n.a 64 2
315.3.o \(\chi_{315}(127, \cdot)\) 315.3.o.a 12 2
315.3.o.b 24
315.3.o.c 24
315.3.q \(\chi_{315}(229, \cdot)\) 315.3.q.a 184 2
315.3.s \(\chi_{315}(11, \cdot)\) 315.3.s.a 128 2
315.3.v \(\chi_{315}(254, \cdot)\) 315.3.v.a 184 2
315.3.w \(\chi_{315}(136, \cdot)\) 315.3.w.a 8 2
315.3.w.b 12
315.3.w.c 12
315.3.w.d 20
315.3.x \(\chi_{315}(76, \cdot)\) 315.3.x.a 128 2
315.3.y \(\chi_{315}(44, \cdot)\) 315.3.y.a 64 2
315.3.ba \(\chi_{315}(29, \cdot)\) 315.3.ba.a 144 2
315.3.bc \(\chi_{315}(31, \cdot)\) 315.3.bc.a 128 2
315.3.bd \(\chi_{315}(191, \cdot)\) 315.3.bd.a 128 2
315.3.bg \(\chi_{315}(34, \cdot)\) 315.3.bg.a 4 2
315.3.bg.b 4
315.3.bg.c 176
315.3.bi \(\chi_{315}(19, \cdot)\) 315.3.bi.a 4 2
315.3.bi.b 4
315.3.bi.c 12
315.3.bi.d 24
315.3.bi.e 32
315.3.bk \(\chi_{315}(176, \cdot)\) 315.3.bk.a 96 2
315.3.bm \(\chi_{315}(116, \cdot)\) 315.3.bm.a 40 2
315.3.bn \(\chi_{315}(94, \cdot)\) 315.3.bn.a 184 2
315.3.bp \(\chi_{315}(166, \cdot)\) 315.3.bp.a 128 2
315.3.br \(\chi_{315}(74, \cdot)\) 315.3.br.a 184 2
315.3.bt \(\chi_{315}(58, \cdot)\) 315.3.bt.a 368 4
315.3.bu \(\chi_{315}(38, \cdot)\) 315.3.bu.a 368 4
315.3.bw \(\chi_{315}(47, \cdot)\) 315.3.bw.a 368 4
315.3.by \(\chi_{315}(22, \cdot)\) 315.3.by.a 288 4
315.3.ca \(\chi_{315}(37, \cdot)\) 315.3.ca.a 24 4
315.3.ca.b 64
315.3.ca.c 64
315.3.cd \(\chi_{315}(17, \cdot)\) 315.3.cd.a 128 4
315.3.cf \(\chi_{315}(83, \cdot)\) 315.3.cf.a 368 4
315.3.ch \(\chi_{315}(67, \cdot)\) 315.3.ch.a 368 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(315))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(315)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 1}\)