Properties

Label 546.8
Level 546
Weight 8
Dimension 13360
Nonzero newspaces 30
Sturm bound 129024
Trace bound 7

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Defining parameters

Level: \( N \) = \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(129024\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(546))\).

Total New Old
Modular forms 57024 13360 43664
Cusp forms 55872 13360 42512
Eisenstein series 1152 0 1152

Trace form

\( 13360q + 32q^{2} + 768q^{4} - 432q^{5} - 1728q^{6} + 248q^{7} - 4096q^{8} + 7140q^{9} + O(q^{10}) \) \( 13360q + 32q^{2} + 768q^{4} - 432q^{5} - 1728q^{6} + 248q^{7} - 4096q^{8} + 7140q^{9} + 33696q^{10} - 30480q^{11} - 13824q^{12} - 117388q^{13} - 3520q^{14} + 194616q^{15} + 81920q^{16} + 383124q^{17} - 60288q^{18} - 962176q^{19} - 51456q^{20} + 486216q^{21} + 234624q^{22} + 424488q^{23} - 122880q^{24} - 1272896q^{25} - 400768q^{26} - 308376q^{27} + 100864q^{28} + 2517468q^{29} + 2264448q^{30} + 2617024q^{31} + 131072q^{32} - 4225632q^{33} - 2097984q^{34} - 4251144q^{35} - 1985280q^{36} + 3452124q^{37} + 554176q^{38} + 7994904q^{39} - 393216q^{40} + 990588q^{41} - 177984q^{42} + 6118384q^{43} + 73728q^{44} - 17970348q^{45} - 3543552q^{46} + 2436696q^{47} - 9161844q^{49} + 184448q^{50} + 4155120q^{51} - 1358848q^{52} - 18056160q^{53} - 11402496q^{54} + 23857944q^{55} + 5292032q^{56} + 15113688q^{57} + 12684192q^{58} + 19143408q^{59} + 2694144q^{60} + 25480060q^{61} - 25344512q^{62} - 9146832q^{63} + 12582912q^{64} - 55189968q^{65} - 12890496q^{66} - 32682192q^{67} + 6803712q^{68} - 5213568q^{69} + 20857920q^{70} + 67039440q^{71} + 21805056q^{72} - 357760q^{73} - 33615968q^{74} + 55781568q^{75} + 65196032q^{76} + 115500552q^{77} - 39558624q^{78} - 76990960q^{79} - 3194880q^{80} + 71369916q^{81} - 135230112q^{82} - 158664192q^{83} - 38217216q^{84} - 43939308q^{85} + 35717440q^{86} + 66145152q^{87} + 11931648q^{88} + 178144344q^{89} + 49828608q^{90} + 303586072q^{91} + 94540800q^{92} + 110557128q^{93} + 46080384q^{94} - 43509672q^{95} - 7864320q^{96} - 549101696q^{97} - 178967776q^{98} + 120276072q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(546))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
546.8.a \(\chi_{546}(1, \cdot)\) 546.8.a.a 1 1
546.8.a.b 1
546.8.a.c 1
546.8.a.d 3
546.8.a.e 3
546.8.a.f 4
546.8.a.g 4
546.8.a.h 5
546.8.a.i 5
546.8.a.j 5
546.8.a.k 5
546.8.a.l 5
546.8.a.m 5
546.8.a.n 6
546.8.a.o 6
546.8.a.p 6
546.8.a.q 6
546.8.a.r 6
546.8.a.s 7
546.8.c \(\chi_{546}(337, \cdot)\) 546.8.c.a 24 1
546.8.c.b 24
546.8.c.c 26
546.8.c.d 26
546.8.e \(\chi_{546}(545, \cdot)\) n/a 264 1
546.8.g \(\chi_{546}(209, \cdot)\) n/a 224 1
546.8.i \(\chi_{546}(79, \cdot)\) n/a 224 2
546.8.j \(\chi_{546}(289, \cdot)\) n/a 260 2
546.8.k \(\chi_{546}(373, \cdot)\) n/a 260 2
546.8.l \(\chi_{546}(211, \cdot)\) n/a 192 2
546.8.o \(\chi_{546}(265, \cdot)\) n/a 256 2
546.8.p \(\chi_{546}(239, \cdot)\) n/a 392 2
546.8.q \(\chi_{546}(251, \cdot)\) n/a 520 2
546.8.s \(\chi_{546}(43, \cdot)\) n/a 200 2
546.8.u \(\chi_{546}(185, \cdot)\) n/a 524 2
546.8.z \(\chi_{546}(131, \cdot)\) n/a 448 2
546.8.bb \(\chi_{546}(269, \cdot)\) n/a 524 2
546.8.bd \(\chi_{546}(121, \cdot)\) n/a 260 2
546.8.bg \(\chi_{546}(311, \cdot)\) n/a 520 2
546.8.bi \(\chi_{546}(17, \cdot)\) n/a 524 2
546.8.bk \(\chi_{546}(25, \cdot)\) n/a 264 2
546.8.bm \(\chi_{546}(205, \cdot)\) n/a 260 2
546.8.bn \(\chi_{546}(101, \cdot)\) n/a 524 2
546.8.bq \(\chi_{546}(419, \cdot)\) n/a 520 2
546.8.bu \(\chi_{546}(71, \cdot)\) n/a 784 4
546.8.bv \(\chi_{546}(317, \cdot)\) n/a 1040 4
546.8.bw \(\chi_{546}(11, \cdot)\) n/a 1048 4
546.8.bx \(\chi_{546}(97, \cdot)\) n/a 528 4
546.8.by \(\chi_{546}(19, \cdot)\) n/a 520 4
546.8.bz \(\chi_{546}(31, \cdot)\) n/a 528 4
546.8.cg \(\chi_{546}(145, \cdot)\) n/a 520 4
546.8.ch \(\chi_{546}(137, \cdot)\) n/a 1048 4

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(546))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(546)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 2}\)