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Properties

Label 616.4
Level 616
Weight 4
Dimension 18142
Nonzero newspaces 24
Sturm bound 92160
Trace bound 8

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Defining parameters

Level: \( N \) = \( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(92160\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(616))\).

Total New Old
Modular forms 35280 18502 16778
Cusp forms 33840 18142 15698
Eisenstein series 1440 360 1080

Trace form

\( 18142 q - 36 q^{2} - 44 q^{3} - 76 q^{4} - 8 q^{5} + 84 q^{6} - 22 q^{7} + 84 q^{8} - 24 q^{9} + O(q^{10}) \) \( 18142 q - 36 q^{2} - 44 q^{3} - 76 q^{4} - 8 q^{5} + 84 q^{6} - 22 q^{7} + 84 q^{8} - 24 q^{9} - 252 q^{10} - 164 q^{11} - 292 q^{12} - 68 q^{13} - 6 q^{14} + 560 q^{15} + 36 q^{16} - 344 q^{18} - 638 q^{19} - 624 q^{20} - 276 q^{21} - 346 q^{22} - 1636 q^{23} + 604 q^{24} - 40 q^{25} + 2592 q^{26} + 2134 q^{27} + 2746 q^{28} + 1492 q^{29} + 1000 q^{30} + 4052 q^{31} - 2796 q^{32} - 1072 q^{33} - 4796 q^{34} - 2012 q^{35} - 4808 q^{36} - 1908 q^{37} - 2500 q^{38} - 2704 q^{39} + 3708 q^{40} - 1156 q^{41} + 6616 q^{42} - 668 q^{43} + 8170 q^{44} - 824 q^{45} + 8468 q^{46} + 5012 q^{47} + 7840 q^{48} - 1566 q^{49} - 2140 q^{50} + 5026 q^{51} - 9812 q^{52} + 6620 q^{53} - 16836 q^{54} + 268 q^{55} - 9868 q^{56} + 3006 q^{57} - 10940 q^{58} + 802 q^{59} - 11420 q^{60} + 1408 q^{61} - 3224 q^{62} - 4580 q^{63} + 3656 q^{64} - 3976 q^{65} + 1634 q^{66} - 15192 q^{67} - 2716 q^{68} - 15800 q^{69} + 2224 q^{70} - 19244 q^{71} + 14788 q^{72} - 12592 q^{73} + 13448 q^{74} - 9566 q^{75} + 12628 q^{76} + 2176 q^{77} + 11688 q^{78} + 7616 q^{79} + 3964 q^{80} + 12302 q^{81} + 796 q^{82} + 31102 q^{83} + 9786 q^{84} + 22088 q^{85} - 6452 q^{86} + 35236 q^{87} - 22666 q^{88} + 11256 q^{89} - 13944 q^{90} + 17412 q^{91} + 1576 q^{92} + 10360 q^{93} - 3364 q^{94} + 8656 q^{95} - 2144 q^{96} - 5674 q^{97} - 5820 q^{98} - 15532 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(616))\)

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
616.4.a \(\chi_{616}(1, \cdot)\) 616.4.a.a 1 1
616.4.a.b 2
616.4.a.c 2
616.4.a.d 2
616.4.a.e 4
616.4.a.f 4
616.4.a.g 5
616.4.a.h 6
616.4.a.i 6
616.4.a.j 7
616.4.a.k 7
616.4.c \(\chi_{616}(309, \cdot)\) n/a 180 1
616.4.e \(\chi_{616}(153, \cdot)\) 616.4.e.a 72 1
616.4.f \(\chi_{616}(351, \cdot)\) None 0 1
616.4.h \(\chi_{616}(419, \cdot)\) n/a 240 1
616.4.j \(\chi_{616}(111, \cdot)\) None 0 1
616.4.l \(\chi_{616}(43, \cdot)\) n/a 216 1
616.4.o \(\chi_{616}(461, \cdot)\) n/a 284 1
616.4.q \(\chi_{616}(177, \cdot)\) n/a 120 2
616.4.r \(\chi_{616}(113, \cdot)\) n/a 216 4
616.4.s \(\chi_{616}(285, \cdot)\) n/a 568 2
616.4.w \(\chi_{616}(199, \cdot)\) None 0 2
616.4.y \(\chi_{616}(219, \cdot)\) n/a 568 2
616.4.ba \(\chi_{616}(263, \cdot)\) None 0 2
616.4.bc \(\chi_{616}(243, \cdot)\) n/a 480 2
616.4.bd \(\chi_{616}(221, \cdot)\) n/a 480 2
616.4.bf \(\chi_{616}(241, \cdot)\) n/a 144 2
616.4.bi \(\chi_{616}(13, \cdot)\) n/a 1136 4
616.4.bl \(\chi_{616}(211, \cdot)\) n/a 864 4
616.4.bn \(\chi_{616}(223, \cdot)\) None 0 4
616.4.bp \(\chi_{616}(27, \cdot)\) n/a 1136 4
616.4.br \(\chi_{616}(127, \cdot)\) None 0 4
616.4.bs \(\chi_{616}(41, \cdot)\) n/a 288 4
616.4.bu \(\chi_{616}(141, \cdot)\) n/a 864 4
616.4.bw \(\chi_{616}(9, \cdot)\) n/a 576 8
616.4.by \(\chi_{616}(17, \cdot)\) n/a 576 8
616.4.ca \(\chi_{616}(37, \cdot)\) n/a 2272 8
616.4.cb \(\chi_{616}(3, \cdot)\) n/a 2272 8
616.4.cd \(\chi_{616}(39, \cdot)\) None 0 8
616.4.cf \(\chi_{616}(51, \cdot)\) n/a 2272 8
616.4.ch \(\chi_{616}(31, \cdot)\) None 0 8
616.4.cl \(\chi_{616}(61, \cdot)\) n/a 2272 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(616))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(616)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 2}\)