Properties

Label 1044.2
Level 1044
Weight 2
Dimension 13687
Nonzero newspaces 24
Sturm bound 120960
Trace bound 22

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Defining parameters

Level: \( N \) = \( 1044 = 2^{2} \cdot 3^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(120960\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1044))\).

Total New Old
Modular forms 31360 14175 17185
Cusp forms 29121 13687 15434
Eisenstein series 2239 488 1751

Trace form

\( 13687 q - 36 q^{2} - 32 q^{4} - 66 q^{5} - 50 q^{6} + 6 q^{7} - 42 q^{8} - 88 q^{9} + O(q^{10}) \) \( 13687 q - 36 q^{2} - 32 q^{4} - 66 q^{5} - 50 q^{6} + 6 q^{7} - 42 q^{8} - 88 q^{9} - 118 q^{10} + 6 q^{11} - 68 q^{12} - 70 q^{13} - 66 q^{14} - 18 q^{15} - 56 q^{16} - 108 q^{17} - 92 q^{18} - 78 q^{20} - 106 q^{21} - 48 q^{22} - 20 q^{23} - 62 q^{24} - 94 q^{25} - 42 q^{26} - 88 q^{28} - 115 q^{29} - 76 q^{30} - 10 q^{31} + 24 q^{32} - 142 q^{33} - 16 q^{34} - 16 q^{35} + 10 q^{36} - 246 q^{37} + 12 q^{38} + 6 q^{39} - 46 q^{40} - 126 q^{41} - 20 q^{42} - 18 q^{43} - 28 q^{44} - 142 q^{45} - 80 q^{46} + 10 q^{47} - 98 q^{48} - 66 q^{49} + 14 q^{50} + 6 q^{52} + 3 q^{53} - 134 q^{54} + 76 q^{55} + 20 q^{56} - 124 q^{57} + 94 q^{58} + 22 q^{59} - 68 q^{60} - 38 q^{61} + 56 q^{62} + 6 q^{63} - 20 q^{64} + 33 q^{65} - 8 q^{66} + 74 q^{67} + 86 q^{68} - 34 q^{69} + 82 q^{70} + 202 q^{71} - 14 q^{72} - 17 q^{73} + 32 q^{74} + 164 q^{75} - 36 q^{76} + 180 q^{77} - 32 q^{78} + 114 q^{79} - 42 q^{80} + 136 q^{81} - 154 q^{82} + 150 q^{83} - 116 q^{84} + 148 q^{85} - 126 q^{86} + 149 q^{87} - 42 q^{88} + 102 q^{89} - 68 q^{90} + 264 q^{91} - 90 q^{92} - 90 q^{93} - 6 q^{94} + 312 q^{95} - 80 q^{96} + 31 q^{97} - 112 q^{98} + 122 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1044))\)

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
1044.2.a \(\chi_{1044}(1, \cdot)\) 1044.2.a.a 1 1
1044.2.a.b 1
1044.2.a.c 1
1044.2.a.d 1
1044.2.a.e 1
1044.2.a.f 1
1044.2.a.g 1
1044.2.a.h 1
1044.2.a.i 1
1044.2.a.j 1
1044.2.a.k 1
1044.2.b \(\chi_{1044}(1043, \cdot)\) 1044.2.b.a 4 1
1044.2.b.b 16
1044.2.b.c 40
1044.2.c \(\chi_{1044}(755, \cdot)\) 1044.2.c.a 56 1
1044.2.h \(\chi_{1044}(289, \cdot)\) 1044.2.h.a 2 1
1044.2.h.b 2
1044.2.h.c 2
1044.2.h.d 2
1044.2.h.e 2
1044.2.h.f 2
1044.2.i \(\chi_{1044}(349, \cdot)\) 1044.2.i.a 22 2
1044.2.i.b 34
1044.2.j \(\chi_{1044}(307, \cdot)\) n/a 146 2
1044.2.m \(\chi_{1044}(17, \cdot)\) 1044.2.m.a 8 2
1044.2.m.b 12
1044.2.n \(\chi_{1044}(637, \cdot)\) 1044.2.n.a 60 2
1044.2.s \(\chi_{1044}(59, \cdot)\) n/a 336 2
1044.2.t \(\chi_{1044}(347, \cdot)\) n/a 352 2
1044.2.u \(\chi_{1044}(181, \cdot)\) 1044.2.u.a 6 6
1044.2.u.b 12
1044.2.u.c 12
1044.2.u.d 12
1044.2.u.e 36
1044.2.v \(\chi_{1044}(41, \cdot)\) n/a 120 4
1044.2.y \(\chi_{1044}(331, \cdot)\) n/a 704 4
1044.2.z \(\chi_{1044}(109, \cdot)\) 1044.2.z.a 6 6
1044.2.z.b 6
1044.2.z.c 24
1044.2.z.d 36
1044.2.be \(\chi_{1044}(107, \cdot)\) n/a 360 6
1044.2.bf \(\chi_{1044}(35, \cdot)\) n/a 360 6
1044.2.bg \(\chi_{1044}(25, \cdot)\) n/a 360 12
1044.2.bh \(\chi_{1044}(89, \cdot)\) n/a 120 12
1044.2.bk \(\chi_{1044}(19, \cdot)\) n/a 876 12
1044.2.bl \(\chi_{1044}(167, \cdot)\) n/a 2112 12
1044.2.bm \(\chi_{1044}(23, \cdot)\) n/a 2112 12
1044.2.br \(\chi_{1044}(13, \cdot)\) n/a 360 12
1044.2.bs \(\chi_{1044}(31, \cdot)\) n/a 4224 24
1044.2.bv \(\chi_{1044}(77, \cdot)\) n/a 720 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1044))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1044)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(522))\)\(^{\oplus 2}\)