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Properties

Label 1035.2
Level 1035
Weight 2
Dimension 26916
Nonzero newspaces 24
Sturm bound 152064
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(152064\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1035))\).

Total New Old
Modular forms 39424 28052 11372
Cusp forms 36609 26916 9693
Eisenstein series 2815 1136 1679

Trace form

\( 26916 q - 52 q^{2} - 72 q^{3} - 44 q^{4} - 81 q^{5} - 232 q^{6} - 42 q^{7} - 60 q^{8} - 80 q^{9} + O(q^{10}) \) \( 26916 q - 52 q^{2} - 72 q^{3} - 44 q^{4} - 81 q^{5} - 232 q^{6} - 42 q^{7} - 60 q^{8} - 80 q^{9} - 267 q^{10} - 190 q^{11} - 104 q^{12} - 62 q^{13} - 90 q^{14} - 140 q^{15} - 140 q^{16} - 48 q^{17} - 120 q^{18} - 136 q^{19} - 105 q^{20} - 264 q^{21} - 16 q^{22} - 34 q^{23} - 248 q^{24} - 83 q^{25} - 182 q^{26} - 120 q^{27} - 126 q^{28} - 88 q^{29} - 196 q^{30} - 160 q^{31} - 48 q^{32} - 104 q^{33} - 50 q^{34} - 61 q^{35} - 200 q^{36} - 114 q^{37} + 76 q^{38} - 24 q^{39} + 35 q^{40} - 54 q^{41} - 16 q^{42} + 86 q^{43} + 92 q^{44} - 76 q^{45} - 378 q^{46} + 36 q^{47} - 8 q^{48} + 60 q^{49} - 15 q^{50} - 232 q^{51} + 150 q^{52} - 26 q^{53} - 168 q^{54} - 343 q^{55} - 532 q^{56} - 252 q^{57} - 272 q^{58} - 374 q^{59} - 392 q^{60} - 514 q^{61} - 630 q^{62} - 428 q^{63} - 824 q^{64} - 454 q^{65} - 792 q^{66} - 246 q^{67} - 1064 q^{68} - 368 q^{69} - 582 q^{70} - 656 q^{71} - 664 q^{72} - 326 q^{73} - 568 q^{74} - 270 q^{75} - 688 q^{76} - 284 q^{77} - 272 q^{78} - 218 q^{79} - 260 q^{80} - 360 q^{81} - 270 q^{82} - 32 q^{83} - 208 q^{84} - 43 q^{85} + 90 q^{86} + 22 q^{88} + 198 q^{89} + 32 q^{90} - 300 q^{91} + 228 q^{92} - 56 q^{93} + 184 q^{94} + 36 q^{95} - 328 q^{96} - 4 q^{97} + 188 q^{98} - 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1035))\)

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
1035.2.a \(\chi_{1035}(1, \cdot)\) 1035.2.a.a 1 1
1035.2.a.b 1
1035.2.a.c 1
1035.2.a.d 1
1035.2.a.e 1
1035.2.a.f 1
1035.2.a.g 1
1035.2.a.h 2
1035.2.a.i 2
1035.2.a.j 2
1035.2.a.k 2
1035.2.a.l 2
1035.2.a.m 2
1035.2.a.n 3
1035.2.a.o 4
1035.2.a.p 6
1035.2.a.q 6
1035.2.b \(\chi_{1035}(829, \cdot)\) 1035.2.b.a 2 1
1035.2.b.b 2
1035.2.b.c 2
1035.2.b.d 6
1035.2.b.e 8
1035.2.b.f 14
1035.2.b.g 20
1035.2.c \(\chi_{1035}(206, \cdot)\) 1035.2.c.a 4 1
1035.2.c.b 4
1035.2.c.c 12
1035.2.c.d 12
1035.2.h \(\chi_{1035}(1034, \cdot)\) 1035.2.h.a 8 1
1035.2.h.b 40
1035.2.i \(\chi_{1035}(346, \cdot)\) 1035.2.i.a 4 2
1035.2.i.b 4
1035.2.i.c 34
1035.2.i.d 38
1035.2.i.e 46
1035.2.i.f 50
1035.2.j \(\chi_{1035}(323, \cdot)\) 1035.2.j.a 44 2
1035.2.j.b 44
1035.2.k \(\chi_{1035}(298, \cdot)\) n/a 116 2
1035.2.n \(\chi_{1035}(344, \cdot)\) n/a 280 2
1035.2.s \(\chi_{1035}(551, \cdot)\) n/a 192 2
1035.2.t \(\chi_{1035}(139, \cdot)\) n/a 264 2
1035.2.u \(\chi_{1035}(271, \cdot)\) n/a 400 10
1035.2.x \(\chi_{1035}(47, \cdot)\) n/a 528 4
1035.2.y \(\chi_{1035}(22, \cdot)\) n/a 560 4
1035.2.z \(\chi_{1035}(44, \cdot)\) n/a 480 10
1035.2.be \(\chi_{1035}(251, \cdot)\) n/a 320 10
1035.2.bf \(\chi_{1035}(64, \cdot)\) n/a 580 10
1035.2.bg \(\chi_{1035}(16, \cdot)\) n/a 1920 20
1035.2.bj \(\chi_{1035}(28, \cdot)\) n/a 1160 20
1035.2.bk \(\chi_{1035}(8, \cdot)\) n/a 960 20
1035.2.bl \(\chi_{1035}(4, \cdot)\) n/a 2800 20
1035.2.bm \(\chi_{1035}(11, \cdot)\) n/a 1920 20
1035.2.br \(\chi_{1035}(14, \cdot)\) n/a 2800 20
1035.2.bs \(\chi_{1035}(7, \cdot)\) n/a 5600 40
1035.2.bt \(\chi_{1035}(2, \cdot)\) n/a 5600 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1035))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1035)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 2}\)