Properties

Label 1110.4
Level 1110
Weight 4
Dimension 22540
Nonzero newspaces 30
Sturm bound 262656
Trace bound 8

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Defining parameters

Level: \( N \) = \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(262656\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1110))\).

Total New Old
Modular forms 99648 22540 77108
Cusp forms 97344 22540 74804
Eisenstein series 2304 0 2304

Trace form

\( 22540q - 28q^{3} - 8q^{5} + 8q^{6} - 80q^{7} + O(q^{10}) \) \( 22540q - 28q^{3} - 8q^{5} + 8q^{6} - 80q^{7} + 80q^{10} - 64q^{11} + 16q^{12} + 304q^{13} + 128q^{14} + 476q^{15} + 256q^{16} + 144q^{17} + 32q^{18} - 32q^{19} + 32q^{20} - 1120q^{21} - 672q^{22} - 144q^{23} - 96q^{24} - 640q^{25} + 2088q^{26} + 2564q^{27} + 1408q^{28} + 3312q^{29} + 264q^{30} - 2496q^{31} - 4384q^{33} - 8192q^{34} - 7792q^{35} - 2320q^{36} - 12664q^{37} - 5760q^{38} - 5496q^{39} - 1968q^{40} - 6160q^{41} + 1312q^{42} + 7024q^{43} + 1984q^{44} + 2728q^{45} + 18368q^{46} + 10944q^{47} + 2368q^{48} + 20976q^{49} + 2980q^{50} - 344q^{51} - 704q^{52} - 288q^{53} - 216q^{54} - 3584q^{55} + 640q^{56} - 2320q^{57} - 5376q^{58} + 16448q^{59} - 2320q^{60} + 13820q^{61} - 2016q^{62} + 4952q^{63} - 2178q^{65} - 352q^{66} - 3776q^{67} + 576q^{68} - 14496q^{69} + 5760q^{70} - 15840q^{71} - 128q^{72} - 21920q^{73} - 80q^{74} - 10328q^{75} + 1408q^{76} - 14112q^{77} + 7728q^{78} - 8240q^{79} - 128q^{80} + 3088q^{81} - 2688q^{82} + 4752q^{83} - 576q^{84} + 10774q^{85} - 2912q^{86} + 15008q^{87} - 2688q^{88} + 27244q^{89} - 10768q^{90} + 28016q^{91} - 576q^{92} - 43744q^{93} - 4864q^{94} + 2352q^{95} + 640q^{96} + 17872q^{97} + 4032q^{98} - 3456q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1110))\)

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
1110.4.a \(\chi_{1110}(1, \cdot)\) 1110.4.a.a 1 1
1110.4.a.b 1
1110.4.a.c 2
1110.4.a.d 2
1110.4.a.e 3
1110.4.a.f 3
1110.4.a.g 3
1110.4.a.h 3
1110.4.a.i 4
1110.4.a.j 4
1110.4.a.k 4
1110.4.a.l 4
1110.4.a.m 5
1110.4.a.n 5
1110.4.a.o 5
1110.4.a.p 5
1110.4.a.q 5
1110.4.a.r 6
1110.4.a.s 7
1110.4.d \(\chi_{1110}(889, \cdot)\) n/a 108 1
1110.4.e \(\chi_{1110}(739, \cdot)\) n/a 116 1
1110.4.h \(\chi_{1110}(961, \cdot)\) 1110.4.h.a 4 1
1110.4.h.b 12
1110.4.h.c 20
1110.4.h.d 20
1110.4.h.e 20
1110.4.i \(\chi_{1110}(121, \cdot)\) n/a 152 2
1110.4.k \(\chi_{1110}(179, \cdot)\) n/a 456 2
1110.4.l \(\chi_{1110}(43, \cdot)\) n/a 228 2
1110.4.m \(\chi_{1110}(593, \cdot)\) n/a 432 2
1110.4.n \(\chi_{1110}(443, \cdot)\) n/a 456 2
1110.4.o \(\chi_{1110}(253, \cdot)\) n/a 228 2
1110.4.u \(\chi_{1110}(191, \cdot)\) n/a 304 2
1110.4.x \(\chi_{1110}(751, \cdot)\) n/a 152 2
1110.4.ba \(\chi_{1110}(529, \cdot)\) n/a 232 2
1110.4.bb \(\chi_{1110}(1009, \cdot)\) n/a 224 2
1110.4.bc \(\chi_{1110}(181, \cdot)\) n/a 456 6
1110.4.be \(\chi_{1110}(251, \cdot)\) n/a 608 4
1110.4.bf \(\chi_{1110}(97, \cdot)\) n/a 456 4
1110.4.bg \(\chi_{1110}(233, \cdot)\) n/a 912 4
1110.4.bh \(\chi_{1110}(47, \cdot)\) n/a 912 4
1110.4.bi \(\chi_{1110}(193, \cdot)\) n/a 456 4
1110.4.bo \(\chi_{1110}(29, \cdot)\) n/a 912 4
1110.4.bp \(\chi_{1110}(139, \cdot)\) n/a 696 6
1110.4.bq \(\chi_{1110}(49, \cdot)\) n/a 672 6
1110.4.br \(\chi_{1110}(151, \cdot)\) n/a 456 6
1110.4.by \(\chi_{1110}(59, \cdot)\) n/a 2736 12
1110.4.bz \(\chi_{1110}(131, \cdot)\) n/a 1824 12
1110.4.cc \(\chi_{1110}(163, \cdot)\) n/a 1368 12
1110.4.cd \(\chi_{1110}(53, \cdot)\) n/a 2736 12
1110.4.cg \(\chi_{1110}(77, \cdot)\) n/a 2736 12
1110.4.ch \(\chi_{1110}(13, \cdot)\) n/a 1368 12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1110))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1110)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(555))\)\(^{\oplus 2}\)