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Properties

Label 924.2
Level 924
Weight 2
Dimension 9316
Nonzero newspaces 32
Newform subspaces 78
Sturm bound 92160
Trace bound 7

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Defining parameters

Level: \( N \) = \( 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Newform subspaces: \( 78 \)
Sturm bound: \(92160\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(924))\).

Total New Old
Modular forms 24240 9684 14556
Cusp forms 21841 9316 12525
Eisenstein series 2399 368 2031

Trace form

\( 9316 q - 2 q^{3} - 28 q^{4} - 12 q^{5} - 8 q^{6} - 26 q^{7} + 12 q^{8} - 38 q^{9} + O(q^{10}) \) \( 9316 q - 2 q^{3} - 28 q^{4} - 12 q^{5} - 8 q^{6} - 26 q^{7} + 12 q^{8} - 38 q^{9} + 28 q^{10} - 14 q^{11} - 4 q^{12} - 32 q^{13} + 58 q^{14} + 36 q^{15} + 100 q^{16} + 44 q^{17} + 36 q^{18} + 92 q^{19} + 100 q^{20} + 50 q^{21} + 8 q^{22} + 64 q^{23} + 28 q^{24} + 84 q^{25} + 40 q^{26} + 34 q^{27} - 84 q^{28} + 112 q^{29} - 70 q^{30} + 48 q^{31} - 60 q^{32} + 37 q^{33} - 208 q^{34} + 8 q^{35} - 190 q^{36} + 108 q^{37} - 136 q^{38} - 6 q^{39} - 228 q^{40} + 72 q^{41} - 186 q^{42} - 80 q^{43} - 164 q^{44} - 8 q^{45} - 188 q^{46} - 56 q^{47} - 238 q^{48} - 126 q^{49} - 224 q^{50} - 52 q^{51} - 188 q^{52} + 52 q^{53} - 266 q^{54} - 40 q^{55} - 76 q^{56} - 170 q^{57} - 60 q^{58} - 36 q^{59} - 234 q^{60} - 40 q^{61} + 59 q^{63} - 16 q^{64} + 72 q^{65} - 132 q^{66} + 140 q^{67} + 72 q^{68} + 44 q^{69} + 24 q^{70} + 160 q^{71} - 130 q^{72} + 116 q^{73} + 32 q^{74} + 70 q^{75} - 72 q^{76} + 130 q^{77} - 80 q^{78} + 144 q^{79} - 76 q^{80} - 46 q^{81} - 72 q^{82} + 144 q^{83} + 128 q^{84} + 12 q^{85} - 28 q^{86} + 126 q^{87} - 240 q^{88} + 16 q^{89} + 250 q^{90} + 190 q^{91} + 108 q^{92} + 80 q^{93} - 92 q^{94} + 156 q^{95} + 182 q^{96} - 72 q^{97} + 84 q^{98} + 234 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(924))\)

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
924.2.a \(\chi_{924}(1, \cdot)\) 924.2.a.a 1 1
924.2.a.b 1
924.2.a.c 1
924.2.a.d 1
924.2.a.e 1
924.2.a.f 1
924.2.a.g 1
924.2.a.h 1
924.2.c \(\chi_{924}(727, \cdot)\) 924.2.c.a 40 1
924.2.c.b 40
924.2.d \(\chi_{924}(197, \cdot)\) 924.2.d.a 8 1
924.2.d.b 16
924.2.f \(\chi_{924}(155, \cdot)\) 924.2.f.a 60 1
924.2.f.b 60
924.2.i \(\chi_{924}(769, \cdot)\) 924.2.i.a 4 1
924.2.i.b 12
924.2.k \(\chi_{924}(43, \cdot)\) 924.2.k.a 4 1
924.2.k.b 4
924.2.k.c 32
924.2.k.d 32
924.2.l \(\chi_{924}(881, \cdot)\) 924.2.l.a 4 1
924.2.l.b 4
924.2.l.c 8
924.2.l.d 12
924.2.n \(\chi_{924}(923, \cdot)\) 924.2.n.a 8 1
924.2.n.b 8
924.2.n.c 8
924.2.n.d 8
924.2.n.e 16
924.2.n.f 24
924.2.n.g 112
924.2.q \(\chi_{924}(529, \cdot)\) 924.2.q.a 2 2
924.2.q.b 2
924.2.q.c 2
924.2.q.d 4
924.2.q.e 8
924.2.q.f 10
924.2.r \(\chi_{924}(169, \cdot)\) 924.2.r.a 4 4
924.2.r.b 4
924.2.r.c 4
924.2.r.d 4
924.2.r.e 16
924.2.r.f 16
924.2.t \(\chi_{924}(89, \cdot)\) 924.2.t.a 52 2
924.2.u \(\chi_{924}(571, \cdot)\) 924.2.u.a 192 2
924.2.y \(\chi_{924}(131, \cdot)\) 924.2.y.a 8 2
924.2.y.b 8
924.2.y.c 352
924.2.ba \(\chi_{924}(65, \cdot)\) 924.2.ba.a 64 2
924.2.bb \(\chi_{924}(199, \cdot)\) 924.2.bb.a 80 2
924.2.bb.b 80
924.2.bd \(\chi_{924}(241, \cdot)\) 924.2.bd.a 32 2
924.2.bg \(\chi_{924}(23, \cdot)\) 924.2.bg.a 160 2
924.2.bg.b 160
924.2.bj \(\chi_{924}(83, \cdot)\) 924.2.bj.a 32 4
924.2.bj.b 704
924.2.bl \(\chi_{924}(125, \cdot)\) 924.2.bl.a 8 4
924.2.bl.b 8
924.2.bl.c 112
924.2.bm \(\chi_{924}(127, \cdot)\) 924.2.bm.a 144 4
924.2.bm.b 144
924.2.bo \(\chi_{924}(13, \cdot)\) 924.2.bo.a 64 4
924.2.br \(\chi_{924}(71, \cdot)\) 924.2.br.a 8 4
924.2.br.b 8
924.2.br.c 560
924.2.bt \(\chi_{924}(29, \cdot)\) 924.2.bt.a 96 4
924.2.bu \(\chi_{924}(223, \cdot)\) 924.2.bu.a 192 4
924.2.bu.b 192
924.2.bw \(\chi_{924}(25, \cdot)\) 924.2.bw.a 64 8
924.2.bw.b 64
924.2.bx \(\chi_{924}(179, \cdot)\) 924.2.bx.a 1472 8
924.2.ca \(\chi_{924}(61, \cdot)\) 924.2.ca.a 128 8
924.2.cc \(\chi_{924}(31, \cdot)\) 924.2.cc.a 384 8
924.2.cc.b 384
924.2.cd \(\chi_{924}(149, \cdot)\) 924.2.cd.a 256 8
924.2.cf \(\chi_{924}(215, \cdot)\) 924.2.cf.a 1472 8
924.2.cj \(\chi_{924}(79, \cdot)\) 924.2.cj.a 768 8
924.2.ck \(\chi_{924}(5, \cdot)\) 924.2.ck.a 256 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(924))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(924)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 2}\)