Properties

Label 1110.2
Level 1110
Weight 2
Dimension 7509
Nonzero newspaces 30
Sturm bound 131328
Trace bound 10

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Defining parameters

Level: \( N \) = \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(131328\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1110))\).

Total New Old
Modular forms 33984 7509 26475
Cusp forms 31681 7509 24172
Eisenstein series 2303 0 2303

Trace form

\( 7509 q + q^{2} + 5 q^{3} + q^{4} + 9 q^{5} + 5 q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 7509 q + q^{2} + 5 q^{3} + q^{4} + 9 q^{5} + 5 q^{6} + 8 q^{7} + q^{8} + q^{9} - 7 q^{10} - 20 q^{11} - 11 q^{12} - 18 q^{13} - 24 q^{14} - 19 q^{15} + q^{16} - 30 q^{17} - 15 q^{18} - 12 q^{19} - 7 q^{20} - 8 q^{21} - 4 q^{22} - 24 q^{23} + 5 q^{24} + 17 q^{25} + 50 q^{26} + 29 q^{27} + 56 q^{28} + 126 q^{29} + 101 q^{30} + 432 q^{31} + q^{32} + 140 q^{33} + 274 q^{34} + 192 q^{35} + 37 q^{36} + 273 q^{37} + 116 q^{38} + 126 q^{39} + 67 q^{40} + 394 q^{41} + 120 q^{42} + 204 q^{43} - 4 q^{44} + 9 q^{45} + 216 q^{46} + 96 q^{47} + 13 q^{48} + 105 q^{49} + 3 q^{50} - 6 q^{51} - 18 q^{52} - 42 q^{53} + 5 q^{54} - 20 q^{55} - 8 q^{56} + 20 q^{57} - 2 q^{58} + 124 q^{59} + 13 q^{60} + 178 q^{61} - 16 q^{62} + 224 q^{63} + q^{64} + 176 q^{65} - 36 q^{66} + 116 q^{67} - 30 q^{68} + 280 q^{69} + 8 q^{70} + 168 q^{71} + 17 q^{72} + 250 q^{73} - 39 q^{74} + 137 q^{75} - 44 q^{76} + 192 q^{77} - 10 q^{78} + 192 q^{79} + 9 q^{80} + 225 q^{81} - 22 q^{82} + 36 q^{83} - 8 q^{84} + 132 q^{85} - 68 q^{86} + 158 q^{87} - 4 q^{88} + 14 q^{89} - 23 q^{90} - 24 q^{92} - 280 q^{93} - 16 q^{94} - 28 q^{95} - 11 q^{96} - 126 q^{97} - 39 q^{98} - 364 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1110))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1110.2.a \(\chi_{1110}(1, \cdot)\) 1110.2.a.a 1 1
1110.2.a.b 1
1110.2.a.c 1
1110.2.a.d 1
1110.2.a.e 1
1110.2.a.f 1
1110.2.a.g 1
1110.2.a.h 1
1110.2.a.i 1
1110.2.a.j 1
1110.2.a.k 1
1110.2.a.l 1
1110.2.a.m 1
1110.2.a.n 1
1110.2.a.o 1
1110.2.a.p 2
1110.2.a.q 2
1110.2.a.r 2
1110.2.a.s 4
1110.2.d \(\chi_{1110}(889, \cdot)\) 1110.2.d.a 2 1
1110.2.d.b 2
1110.2.d.c 2
1110.2.d.d 2
1110.2.d.e 2
1110.2.d.f 4
1110.2.d.g 4
1110.2.d.h 4
1110.2.d.i 6
1110.2.d.j 8
1110.2.e \(\chi_{1110}(739, \cdot)\) 1110.2.e.a 2 1
1110.2.e.b 2
1110.2.e.c 16
1110.2.e.d 16
1110.2.h \(\chi_{1110}(961, \cdot)\) 1110.2.h.a 2 1
1110.2.h.b 2
1110.2.h.c 2
1110.2.h.d 4
1110.2.h.e 4
1110.2.h.f 6
1110.2.h.g 8
1110.2.i \(\chi_{1110}(121, \cdot)\) 1110.2.i.a 2 2
1110.2.i.b 2
1110.2.i.c 2
1110.2.i.d 2
1110.2.i.e 2
1110.2.i.f 2
1110.2.i.g 2
1110.2.i.h 2
1110.2.i.i 4
1110.2.i.j 4
1110.2.i.k 4
1110.2.i.l 4
1110.2.i.m 4
1110.2.i.n 4
1110.2.i.o 6
1110.2.i.p 10
1110.2.k \(\chi_{1110}(179, \cdot)\) n/a 152 2
1110.2.l \(\chi_{1110}(43, \cdot)\) 1110.2.l.a 36 2
1110.2.l.b 40
1110.2.m \(\chi_{1110}(593, \cdot)\) n/a 144 2
1110.2.n \(\chi_{1110}(443, \cdot)\) n/a 152 2
1110.2.o \(\chi_{1110}(253, \cdot)\) 1110.2.o.a 36 2
1110.2.o.b 40
1110.2.u \(\chi_{1110}(191, \cdot)\) 1110.2.u.a 4 2
1110.2.u.b 4
1110.2.u.c 4
1110.2.u.d 4
1110.2.u.e 40
1110.2.u.f 40
1110.2.x \(\chi_{1110}(751, \cdot)\) 1110.2.x.a 4 2
1110.2.x.b 4
1110.2.x.c 16
1110.2.x.d 16
1110.2.x.e 16
1110.2.ba \(\chi_{1110}(529, \cdot)\) 1110.2.ba.a 36 2
1110.2.ba.b 36
1110.2.bb \(\chi_{1110}(1009, \cdot)\) 1110.2.bb.a 4 2
1110.2.bb.b 4
1110.2.bb.c 4
1110.2.bb.d 28
1110.2.bb.e 40
1110.2.bc \(\chi_{1110}(181, \cdot)\) n/a 144 6
1110.2.be \(\chi_{1110}(251, \cdot)\) n/a 192 4
1110.2.bf \(\chi_{1110}(97, \cdot)\) n/a 152 4
1110.2.bg \(\chi_{1110}(233, \cdot)\) n/a 304 4
1110.2.bh \(\chi_{1110}(47, \cdot)\) n/a 304 4
1110.2.bi \(\chi_{1110}(193, \cdot)\) n/a 152 4
1110.2.bo \(\chi_{1110}(29, \cdot)\) n/a 304 4
1110.2.bp \(\chi_{1110}(139, \cdot)\) n/a 216 6
1110.2.bq \(\chi_{1110}(49, \cdot)\) n/a 240 6
1110.2.br \(\chi_{1110}(151, \cdot)\) n/a 144 6
1110.2.by \(\chi_{1110}(59, \cdot)\) n/a 912 12
1110.2.bz \(\chi_{1110}(131, \cdot)\) n/a 624 12
1110.2.cc \(\chi_{1110}(163, \cdot)\) n/a 456 12
1110.2.cd \(\chi_{1110}(53, \cdot)\) n/a 912 12
1110.2.cg \(\chi_{1110}(77, \cdot)\) n/a 912 12
1110.2.ch \(\chi_{1110}(13, \cdot)\) n/a 456 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1110))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1110)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(555))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1110))\)\(^{\oplus 1}\)