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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

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

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 the 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

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