Properties

Label 1104.6
Level 1104
Weight 6
Dimension 70820
Nonzero newspaces 16
Sturm bound 405504
Trace bound 10

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Defining parameters

Level: \( N \) = \( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(405504\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1104))\).

Total New Old
Modular forms 170192 71200 98992
Cusp forms 167728 70820 96908
Eisenstein series 2464 380 2084

Trace form

\( 70820 q - 47 q^{3} - 168 q^{4} - 76 q^{5} + 188 q^{6} + 270 q^{7} + 984 q^{8} - 953 q^{9} + O(q^{10}) \) \( 70820 q - 47 q^{3} - 168 q^{4} - 76 q^{5} + 188 q^{6} + 270 q^{7} + 984 q^{8} - 953 q^{9} - 1816 q^{10} - 3624 q^{11} - 28 q^{12} + 374 q^{13} - 648 q^{14} + 4467 q^{15} - 8440 q^{16} - 404 q^{17} + 8756 q^{18} - 19426 q^{19} + 15200 q^{20} - 3999 q^{21} - 2504 q^{22} + 4664 q^{23} - 15664 q^{24} + 3888 q^{25} + 25960 q^{26} + 5977 q^{27} + 3752 q^{28} + 16708 q^{29} + 1436 q^{30} - 40738 q^{31} - 88320 q^{32} - 15283 q^{33} - 62312 q^{34} + 38352 q^{35} + 64692 q^{36} + 25382 q^{37} + 144176 q^{38} + 80315 q^{39} + 180760 q^{40} + 21756 q^{41} + 5884 q^{42} - 44418 q^{43} - 87536 q^{44} - 65120 q^{45} - 122072 q^{46} - 70272 q^{47} - 71276 q^{48} - 162148 q^{49} - 212424 q^{50} - 59013 q^{51} + 329672 q^{52} + 223636 q^{53} + 68076 q^{54} + 198014 q^{55} + 317184 q^{56} + 85189 q^{57} + 70680 q^{58} + 61064 q^{59} + 71844 q^{60} - 114314 q^{61} - 382200 q^{62} - 37617 q^{63} - 715992 q^{64} - 60552 q^{65} - 310468 q^{66} - 403362 q^{67} + 244672 q^{68} - 101843 q^{69} + 747808 q^{70} - 60784 q^{71} + 90380 q^{72} - 270338 q^{73} + 189992 q^{74} + 1052135 q^{75} - 484536 q^{76} - 151976 q^{77} - 426332 q^{78} - 529182 q^{79} - 1246736 q^{80} - 365081 q^{81} + 333688 q^{82} - 363732 q^{83} + 10148 q^{84} + 640706 q^{85} + 1162336 q^{86} + 471633 q^{87} + 1179944 q^{88} + 1398508 q^{89} + 127332 q^{90} + 1360496 q^{91} + 12752 q^{92} + 4550 q^{93} - 1021928 q^{94} + 1007096 q^{95} + 19652 q^{96} - 998722 q^{97} - 955472 q^{98} - 729835 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1104))\)

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
1104.6.a \(\chi_{1104}(1, \cdot)\) 1104.6.a.a 1 1
1104.6.a.b 1
1104.6.a.c 1
1104.6.a.d 1
1104.6.a.e 1
1104.6.a.f 2
1104.6.a.g 2
1104.6.a.h 2
1104.6.a.i 3
1104.6.a.j 3
1104.6.a.k 3
1104.6.a.l 4
1104.6.a.m 4
1104.6.a.n 4
1104.6.a.o 4
1104.6.a.p 4
1104.6.a.q 5
1104.6.a.r 5
1104.6.a.s 6
1104.6.a.t 6
1104.6.a.u 6
1104.6.a.v 6
1104.6.a.w 6
1104.6.a.x 7
1104.6.a.y 7
1104.6.a.z 8
1104.6.a.ba 8
1104.6.b \(\chi_{1104}(137, \cdot)\) None 0 1
1104.6.e \(\chi_{1104}(47, \cdot)\) n/a 220 1
1104.6.f \(\chi_{1104}(553, \cdot)\) None 0 1
1104.6.i \(\chi_{1104}(367, \cdot)\) n/a 120 1
1104.6.j \(\chi_{1104}(599, \cdot)\) None 0 1
1104.6.m \(\chi_{1104}(689, \cdot)\) n/a 238 1
1104.6.n \(\chi_{1104}(919, \cdot)\) None 0 1
1104.6.q \(\chi_{1104}(91, \cdot)\) n/a 960 2
1104.6.t \(\chi_{1104}(277, \cdot)\) n/a 880 2
1104.6.u \(\chi_{1104}(323, \cdot)\) n/a 1760 2
1104.6.x \(\chi_{1104}(413, \cdot)\) n/a 1912 2
1104.6.y \(\chi_{1104}(49, \cdot)\) n/a 1200 10
1104.6.bb \(\chi_{1104}(7, \cdot)\) None 0 10
1104.6.bc \(\chi_{1104}(17, \cdot)\) n/a 2380 10
1104.6.bf \(\chi_{1104}(71, \cdot)\) None 0 10
1104.6.bg \(\chi_{1104}(79, \cdot)\) n/a 1200 10
1104.6.bj \(\chi_{1104}(25, \cdot)\) None 0 10
1104.6.bk \(\chi_{1104}(95, \cdot)\) n/a 2400 10
1104.6.bn \(\chi_{1104}(89, \cdot)\) None 0 10
1104.6.bo \(\chi_{1104}(5, \cdot)\) n/a 19120 20
1104.6.br \(\chi_{1104}(35, \cdot)\) n/a 19120 20
1104.6.bs \(\chi_{1104}(13, \cdot)\) n/a 9600 20
1104.6.bv \(\chi_{1104}(19, \cdot)\) n/a 9600 20

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1104))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(1104)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 2}\)