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Properties

Label 1104.2
Level 1104
Weight 2
Dimension 14012
Nonzero newspaces 16
Sturm bound 135168
Trace bound 10

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Defining parameters

Level: \( N \) = \( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(135168\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1104))\).

Total New Old
Modular forms 35024 14392 20632
Cusp forms 32561 14012 18549
Eisenstein series 2463 380 2083

Trace form

\( 14012 q - 31 q^{3} - 72 q^{4} + 4 q^{5} - 28 q^{6} - 50 q^{7} + 24 q^{8} - q^{9} + O(q^{10}) \) \( 14012 q - 31 q^{3} - 72 q^{4} + 4 q^{5} - 28 q^{6} - 50 q^{7} + 24 q^{8} - q^{9} - 72 q^{10} + 24 q^{11} - 44 q^{12} - 90 q^{13} - 24 q^{14} - 13 q^{15} - 120 q^{16} - 4 q^{17} - 60 q^{18} - 34 q^{19} - 32 q^{20} - 63 q^{21} - 120 q^{22} - 8 q^{23} - 144 q^{24} - 40 q^{25} - 40 q^{26} - 55 q^{27} - 88 q^{28} + 20 q^{29} - 84 q^{30} - 98 q^{31} - 83 q^{33} - 72 q^{34} - 48 q^{35} - 76 q^{36} - 42 q^{37} + 16 q^{38} - 69 q^{39} - 40 q^{40} + 12 q^{41} + 44 q^{42} - 66 q^{43} + 80 q^{44} - 16 q^{45} - 40 q^{46} + 84 q^{48} - 108 q^{49} + 72 q^{50} - 101 q^{51} - 24 q^{52} - 28 q^{53} + 52 q^{54} - 130 q^{55} + 5 q^{57} - 120 q^{58} - 56 q^{59} - 60 q^{60} - 218 q^{61} + 24 q^{62} - 49 q^{63} - 216 q^{64} + 24 q^{65} - 148 q^{66} - 98 q^{67} - 64 q^{68} - 83 q^{69} - 320 q^{70} + 16 q^{71} - 116 q^{72} - 82 q^{73} - 104 q^{74} + 71 q^{75} - 216 q^{76} + 56 q^{77} - 140 q^{78} + 98 q^{79} - 16 q^{80} + 63 q^{81} - 136 q^{82} + 204 q^{83} - 28 q^{84} + 130 q^{85} + 32 q^{86} + 273 q^{87} - 24 q^{88} + 188 q^{89} + 4 q^{90} + 304 q^{91} + 16 q^{92} + 54 q^{93} - 8 q^{94} + 376 q^{95} + 68 q^{96} + 46 q^{97} + 80 q^{98} + 293 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1104))\)

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
1104.2.a \(\chi_{1104}(1, \cdot)\) 1104.2.a.a 1 1
1104.2.a.b 1
1104.2.a.c 1
1104.2.a.d 1
1104.2.a.e 1
1104.2.a.f 1
1104.2.a.g 1
1104.2.a.h 1
1104.2.a.i 1
1104.2.a.j 2
1104.2.a.k 2
1104.2.a.l 2
1104.2.a.m 2
1104.2.a.n 2
1104.2.a.o 3
1104.2.b \(\chi_{1104}(137, \cdot)\) None 0 1
1104.2.e \(\chi_{1104}(47, \cdot)\) 1104.2.e.a 2 1
1104.2.e.b 2
1104.2.e.c 4
1104.2.e.d 4
1104.2.e.e 8
1104.2.e.f 8
1104.2.e.g 8
1104.2.e.h 8
1104.2.f \(\chi_{1104}(553, \cdot)\) None 0 1
1104.2.i \(\chi_{1104}(367, \cdot)\) 1104.2.i.a 8 1
1104.2.i.b 16
1104.2.j \(\chi_{1104}(599, \cdot)\) None 0 1
1104.2.m \(\chi_{1104}(689, \cdot)\) 1104.2.m.a 6 1
1104.2.m.b 8
1104.2.m.c 8
1104.2.m.d 8
1104.2.m.e 16
1104.2.n \(\chi_{1104}(919, \cdot)\) None 0 1
1104.2.q \(\chi_{1104}(91, \cdot)\) n/a 192 2
1104.2.t \(\chi_{1104}(277, \cdot)\) n/a 176 2
1104.2.u \(\chi_{1104}(323, \cdot)\) n/a 352 2
1104.2.x \(\chi_{1104}(413, \cdot)\) n/a 376 2
1104.2.y \(\chi_{1104}(49, \cdot)\) n/a 240 10
1104.2.bb \(\chi_{1104}(7, \cdot)\) None 0 10
1104.2.bc \(\chi_{1104}(17, \cdot)\) n/a 460 10
1104.2.bf \(\chi_{1104}(71, \cdot)\) None 0 10
1104.2.bg \(\chi_{1104}(79, \cdot)\) n/a 240 10
1104.2.bj \(\chi_{1104}(25, \cdot)\) None 0 10
1104.2.bk \(\chi_{1104}(95, \cdot)\) n/a 480 10
1104.2.bn \(\chi_{1104}(89, \cdot)\) None 0 10
1104.2.bo \(\chi_{1104}(5, \cdot)\) n/a 3760 20
1104.2.br \(\chi_{1104}(35, \cdot)\) n/a 3760 20
1104.2.bs \(\chi_{1104}(13, \cdot)\) n/a 1920 20
1104.2.bv \(\chi_{1104}(19, \cdot)\) n/a 1920 20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1104))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1104)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 2}\)