Properties

Label 504.3
Level 504
Weight 3
Dimension 5810
Nonzero newspaces 30
Sturm bound 41472
Trace bound 25

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(41472\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(504))\).

Total New Old
Modular forms 14400 5990 8410
Cusp forms 13248 5810 7438
Eisenstein series 1152 180 972

Trace form

\( 5810 q - 10 q^{2} - 12 q^{3} - 22 q^{4} - 32 q^{6} - 40 q^{7} - 88 q^{8} - 60 q^{9} + O(q^{10}) \) \( 5810 q - 10 q^{2} - 12 q^{3} - 22 q^{4} - 32 q^{6} - 40 q^{7} - 88 q^{8} - 60 q^{9} - 70 q^{10} - 74 q^{11} + 4 q^{12} + 32 q^{13} + 60 q^{14} - 60 q^{15} + 226 q^{16} - 56 q^{17} + 168 q^{18} - 142 q^{19} + 156 q^{20} + 36 q^{21} - 110 q^{22} + 66 q^{23} + 24 q^{24} - 74 q^{25} - 96 q^{26} + 336 q^{27} - 174 q^{28} + 216 q^{29} + 124 q^{30} + 126 q^{31} - 40 q^{32} - 196 q^{33} + 30 q^{34} + 6 q^{35} - 52 q^{36} - 204 q^{37} + 400 q^{38} - 108 q^{39} + 784 q^{40} - 380 q^{41} - 218 q^{42} + 192 q^{43} - 14 q^{44} - 328 q^{45} + 296 q^{46} - 618 q^{47} - 688 q^{48} - 254 q^{49} - 886 q^{50} - 84 q^{51} - 604 q^{52} + 396 q^{53} - 552 q^{54} - 520 q^{55} - 684 q^{56} + 484 q^{57} - 708 q^{58} + 418 q^{59} - 1128 q^{60} + 404 q^{61} - 756 q^{62} + 466 q^{63} + 386 q^{64} + 1488 q^{65} + 64 q^{66} + 938 q^{67} + 982 q^{68} + 712 q^{69} + 1552 q^{70} + 1428 q^{71} + 1584 q^{72} + 684 q^{73} + 2238 q^{74} - 68 q^{75} + 1130 q^{76} + 1684 q^{78} + 738 q^{79} + 2256 q^{80} - 772 q^{81} + 146 q^{82} - 200 q^{83} + 712 q^{84} + 256 q^{85} + 1006 q^{86} - 732 q^{87} + 154 q^{88} - 164 q^{89} + 880 q^{90} + 84 q^{91} + 6 q^{92} - 16 q^{93} - 126 q^{94} + 30 q^{95} - 432 q^{96} - 540 q^{97} - 1462 q^{98} - 180 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(504))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
504.3.d \(\chi_{504}(449, \cdot)\) 504.3.d.a 4 1
504.3.d.b 8
504.3.e \(\chi_{504}(251, \cdot)\) 504.3.e.a 8 1
504.3.e.b 8
504.3.e.c 48
504.3.f \(\chi_{504}(433, \cdot)\) 504.3.f.a 4 1
504.3.f.b 8
504.3.f.c 8
504.3.g \(\chi_{504}(379, \cdot)\) 504.3.g.a 4 1
504.3.g.b 8
504.3.g.c 24
504.3.g.d 24
504.3.l \(\chi_{504}(181, \cdot)\) 504.3.l.a 2 1
504.3.l.b 2
504.3.l.c 2
504.3.l.d 4
504.3.l.e 4
504.3.l.f 8
504.3.l.g 24
504.3.l.h 32
504.3.m \(\chi_{504}(127, \cdot)\) None 0 1
504.3.n \(\chi_{504}(197, \cdot)\) 504.3.n.a 48 1
504.3.o \(\chi_{504}(503, \cdot)\) None 0 1
504.3.u \(\chi_{504}(59, \cdot)\) n/a 376 2
504.3.v \(\chi_{504}(65, \cdot)\) 504.3.v.a 96 2
504.3.ba \(\chi_{504}(67, \cdot)\) n/a 376 2
504.3.bb \(\chi_{504}(313, \cdot)\) 504.3.bb.a 96 2
504.3.bc \(\chi_{504}(143, \cdot)\) None 0 2
504.3.bd \(\chi_{504}(53, \cdot)\) n/a 128 2
504.3.bg \(\chi_{504}(29, \cdot)\) n/a 288 2
504.3.bh \(\chi_{504}(383, \cdot)\) None 0 2
504.3.bi \(\chi_{504}(149, \cdot)\) n/a 376 2
504.3.bj \(\chi_{504}(167, \cdot)\) None 0 2
504.3.bn \(\chi_{504}(13, \cdot)\) n/a 376 2
504.3.bo \(\chi_{504}(151, \cdot)\) None 0 2
504.3.bp \(\chi_{504}(229, \cdot)\) n/a 376 2
504.3.bq \(\chi_{504}(295, \cdot)\) None 0 2
504.3.bv \(\chi_{504}(415, \cdot)\) None 0 2
504.3.bw \(\chi_{504}(325, \cdot)\) n/a 156 2
504.3.bx \(\chi_{504}(163, \cdot)\) n/a 156 2
504.3.by \(\chi_{504}(73, \cdot)\) 504.3.by.a 8 2
504.3.by.b 8
504.3.by.c 8
504.3.by.d 16
504.3.cd \(\chi_{504}(97, \cdot)\) 504.3.cd.a 96 2
504.3.ce \(\chi_{504}(403, \cdot)\) n/a 376 2
504.3.cf \(\chi_{504}(241, \cdot)\) 504.3.cf.a 96 2
504.3.cg \(\chi_{504}(43, \cdot)\) n/a 288 2
504.3.cl \(\chi_{504}(113, \cdot)\) 504.3.cl.a 72 2
504.3.cm \(\chi_{504}(131, \cdot)\) n/a 376 2
504.3.cn \(\chi_{504}(137, \cdot)\) 504.3.cn.a 96 2
504.3.co \(\chi_{504}(83, \cdot)\) n/a 376 2
504.3.ct \(\chi_{504}(395, \cdot)\) n/a 128 2
504.3.cu \(\chi_{504}(233, \cdot)\) 504.3.cu.a 16 2
504.3.cu.b 16
504.3.cv \(\chi_{504}(79, \cdot)\) None 0 2
504.3.cw \(\chi_{504}(61, \cdot)\) n/a 376 2
504.3.da \(\chi_{504}(47, \cdot)\) None 0 2
504.3.db \(\chi_{504}(221, \cdot)\) n/a 376 2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(504))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(504)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)