↑

Properties

Label 504.6
Level 504
Weight 6
Dimension 14658
Nonzero newspaces 30
Sturm bound 82944
Trace bound 25

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(82944\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(504))\).

Total New Old
Modular forms 35136 14838 20298
Cusp forms 33984 14658 19326
Eisenstein series 1152 180 972

Trace form

\( 14658 q - 10 q^{2} + 6 q^{3} - 54 q^{4} - 52 q^{5} + 112 q^{6} - 136 q^{7} - 1240 q^{8} + 282 q^{9} + O(q^{10}) \) \( 14658 q - 10 q^{2} + 6 q^{3} - 54 q^{4} - 52 q^{5} + 112 q^{6} - 136 q^{7} - 1240 q^{8} + 282 q^{9} + 970 q^{10} + 2162 q^{11} + 2164 q^{12} - 942 q^{13} + 220 q^{14} - 960 q^{15} - 8478 q^{16} - 118 q^{17} + 8952 q^{18} - 3658 q^{19} - 268 q^{20} - 2268 q^{21} - 24846 q^{22} + 19860 q^{23} - 18120 q^{24} + 24400 q^{25} - 7552 q^{26} + 6600 q^{27} + 37586 q^{28} - 25560 q^{29} + 77308 q^{30} + 3664 q^{31} - 35360 q^{32} - 15010 q^{33} - 55426 q^{34} - 79446 q^{35} - 133684 q^{36} + 17610 q^{37} + 58384 q^{38} + 77508 q^{39} + 75928 q^{40} + 20162 q^{41} + 96046 q^{42} + 38282 q^{43} + 49170 q^{44} - 3172 q^{45} + 8304 q^{46} - 246804 q^{47} - 282496 q^{48} - 123786 q^{49} - 266686 q^{50} - 123294 q^{51} - 159852 q^{52} - 25378 q^{53} + 88584 q^{54} + 398528 q^{55} + 120052 q^{56} - 44606 q^{57} + 374860 q^{58} + 424784 q^{59} - 128568 q^{60} + 10476 q^{61} - 152156 q^{62} + 42856 q^{63} + 491346 q^{64} - 93440 q^{65} - 223424 q^{66} - 541414 q^{67} - 863682 q^{68} - 159488 q^{69} - 249848 q^{70} - 345728 q^{71} + 1001520 q^{72} + 73758 q^{73} + 1340990 q^{74} + 230674 q^{75} + 500330 q^{76} + 151302 q^{77} - 640988 q^{78} - 20720 q^{79} - 1307304 q^{80} - 19186 q^{81} + 8210 q^{82} + 83002 q^{83} - 1283336 q^{84} - 537144 q^{85} - 169954 q^{86} + 178728 q^{87} - 25158 q^{88} + 457154 q^{89} - 16112 q^{90} + 389742 q^{91} + 80502 q^{92} + 888716 q^{93} + 631890 q^{94} + 306800 q^{95} + 1757088 q^{96} - 516798 q^{97} + 1291010 q^{98} - 113364 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(504))\)

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
504.6.a \(\chi_{504}(1, \cdot)\) 504.6.a.a 1 1
504.6.a.b 1
504.6.a.c 1
504.6.a.d 1
504.6.a.e 1
504.6.a.f 1
504.6.a.g 1
504.6.a.h 1
504.6.a.i 2
504.6.a.j 2
504.6.a.k 2
504.6.a.l 2
504.6.a.m 2
504.6.a.n 2
504.6.a.o 2
504.6.a.p 2
504.6.a.q 2
504.6.a.r 2
504.6.a.s 2
504.6.a.t 2
504.6.a.u 2
504.6.a.v 2
504.6.a.w 2
504.6.b \(\chi_{504}(55, \cdot)\) None 0 1
504.6.c \(\chi_{504}(253, \cdot)\) n/a 150 1
504.6.h \(\chi_{504}(71, \cdot)\) None 0 1
504.6.i \(\chi_{504}(125, \cdot)\) n/a 160 1
504.6.j \(\chi_{504}(323, \cdot)\) n/a 120 1
504.6.k \(\chi_{504}(377, \cdot)\) 504.6.k.a 40 1
504.6.p \(\chi_{504}(307, \cdot)\) n/a 198 1
504.6.q \(\chi_{504}(25, \cdot)\) n/a 240 2
504.6.r \(\chi_{504}(169, \cdot)\) n/a 180 2
504.6.s \(\chi_{504}(289, \cdot)\) 504.6.s.a 8 2
504.6.s.b 10
504.6.s.c 10
504.6.s.d 10
504.6.s.e 10
504.6.s.f 12
504.6.s.g 20
504.6.s.h 20
504.6.t \(\chi_{504}(193, \cdot)\) n/a 240 2
504.6.w \(\chi_{504}(205, \cdot)\) n/a 952 2
504.6.x \(\chi_{504}(31, \cdot)\) None 0 2
504.6.y \(\chi_{504}(173, \cdot)\) n/a 952 2
504.6.z \(\chi_{504}(95, \cdot)\) None 0 2
504.6.be \(\chi_{504}(139, \cdot)\) n/a 952 2
504.6.bf \(\chi_{504}(115, \cdot)\) n/a 952 2
504.6.bk \(\chi_{504}(19, \cdot)\) n/a 396 2
504.6.bl \(\chi_{504}(17, \cdot)\) 504.6.bl.a 80 2
504.6.bm \(\chi_{504}(107, \cdot)\) n/a 320 2
504.6.br \(\chi_{504}(155, \cdot)\) n/a 720 2
504.6.bs \(\chi_{504}(257, \cdot)\) n/a 240 2
504.6.bt \(\chi_{504}(11, \cdot)\) n/a 952 2
504.6.bu \(\chi_{504}(41, \cdot)\) n/a 240 2
504.6.bz \(\chi_{504}(239, \cdot)\) None 0 2
504.6.ca \(\chi_{504}(5, \cdot)\) n/a 952 2
504.6.cb \(\chi_{504}(23, \cdot)\) None 0 2
504.6.cc \(\chi_{504}(293, \cdot)\) n/a 952 2
504.6.ch \(\chi_{504}(269, \cdot)\) n/a 320 2
504.6.ci \(\chi_{504}(359, \cdot)\) None 0 2
504.6.cj \(\chi_{504}(37, \cdot)\) n/a 396 2
504.6.ck \(\chi_{504}(199, \cdot)\) None 0 2
504.6.cp \(\chi_{504}(223, \cdot)\) None 0 2
504.6.cq \(\chi_{504}(277, \cdot)\) n/a 952 2
504.6.cr \(\chi_{504}(103, \cdot)\) None 0 2
504.6.cs \(\chi_{504}(85, \cdot)\) n/a 720 2
504.6.cx \(\chi_{504}(185, \cdot)\) n/a 240 2
504.6.cy \(\chi_{504}(347, \cdot)\) n/a 952 2
504.6.cz \(\chi_{504}(187, \cdot)\) n/a 952 2

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(504))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(504)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 1}\)