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Properties

Label 1290.2
Level 1290
Weight 2
Dimension 10149
Nonzero newspaces 24
Sturm bound 177408
Trace bound 6

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Defining parameters

Level: \( N \) = \( 1290 = 2 \cdot 3 \cdot 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(177408\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1290))\).

Total New Old
Modular forms 45696 10149 35547
Cusp forms 43009 10149 32860
Eisenstein series 2687 0 2687

Trace form

\( 10149 q + q^{2} + 5 q^{3} + q^{4} + 9 q^{5} + 5 q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 10149 q + q^{2} + 5 q^{3} + q^{4} + 9 q^{5} + 5 q^{6} + 8 q^{7} + q^{8} + q^{9} - 7 q^{10} - 20 q^{11} - 11 q^{12} - 18 q^{13} - 24 q^{14} - 19 q^{15} + q^{16} - 30 q^{17} - 15 q^{18} - 12 q^{19} - 7 q^{20} - 8 q^{21} - 4 q^{22} - 24 q^{23} + 5 q^{24} + 17 q^{25} + 14 q^{26} + 5 q^{27} + 8 q^{28} - 18 q^{29} + 29 q^{30} + 56 q^{31} + q^{32} + 164 q^{33} + 238 q^{34} + 144 q^{35} + 29 q^{36} + 246 q^{37} + 308 q^{38} + 154 q^{39} - 23 q^{40} + 130 q^{41} + 144 q^{42} + 777 q^{43} + 164 q^{44} + 93 q^{45} + 264 q^{46} + 120 q^{47} - 11 q^{48} + 305 q^{49} + 153 q^{50} + 162 q^{51} + 206 q^{52} + 294 q^{53} + 5 q^{54} + 148 q^{55} - 8 q^{56} + 48 q^{57} - 2 q^{58} - 20 q^{59} + 13 q^{60} - 2 q^{61} - 16 q^{62} + 8 q^{63} + q^{64} + 14 q^{65} - 36 q^{66} - 28 q^{67} - 30 q^{68} + 76 q^{69} + 8 q^{70} + 48 q^{71} + 17 q^{72} + 130 q^{73} - 42 q^{74} - q^{75} - 44 q^{76} + 408 q^{77} - 10 q^{78} + 240 q^{79} + 9 q^{80} + 273 q^{81} - 22 q^{82} + 228 q^{83} - 8 q^{84} + 138 q^{85} - 55 q^{86} + 362 q^{87} - 4 q^{88} + 170 q^{89} - 23 q^{90} + 192 q^{91} - 24 q^{92} + 272 q^{93} - 16 q^{94} + 140 q^{95} - 11 q^{96} + 378 q^{97} - 39 q^{98} + 290 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1290))\)

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
1290.2.a \(\chi_{1290}(1, \cdot)\) 1290.2.a.a 1 1
1290.2.a.b 1
1290.2.a.c 1
1290.2.a.d 1
1290.2.a.e 1
1290.2.a.f 1
1290.2.a.g 1
1290.2.a.h 1
1290.2.a.i 1
1290.2.a.j 1
1290.2.a.k 1
1290.2.a.l 1
1290.2.a.m 1
1290.2.a.n 1
1290.2.a.o 2
1290.2.a.p 2
1290.2.a.q 2
1290.2.a.r 2
1290.2.a.s 2
1290.2.a.t 2
1290.2.a.u 3
1290.2.c \(\chi_{1290}(1031, \cdot)\) 1290.2.c.a 2 1
1290.2.c.b 2
1290.2.c.c 2
1290.2.c.d 2
1290.2.c.e 2
1290.2.c.f 2
1290.2.c.g 2
1290.2.c.h 2
1290.2.c.i 10
1290.2.c.j 10
1290.2.c.k 10
1290.2.c.l 10
1290.2.d \(\chi_{1290}(259, \cdot)\) 1290.2.d.a 2 1
1290.2.d.b 2
1290.2.d.c 2
1290.2.d.d 2
1290.2.d.e 2
1290.2.d.f 2
1290.2.d.g 6
1290.2.d.h 8
1290.2.d.i 14
1290.2.f \(\chi_{1290}(1289, \cdot)\) 1290.2.f.a 88 1
1290.2.i \(\chi_{1290}(1081, \cdot)\) 1290.2.i.a 2 2
1290.2.i.b 2
1290.2.i.c 2
1290.2.i.d 2
1290.2.i.e 2
1290.2.i.f 2
1290.2.i.g 2
1290.2.i.h 4
1290.2.i.i 4
1290.2.i.j 4
1290.2.i.k 4
1290.2.i.l 4
1290.2.i.m 4
1290.2.i.n 4
1290.2.i.o 6
1290.2.i.p 8
1290.2.j \(\chi_{1290}(173, \cdot)\) n/a 168 2
1290.2.m \(\chi_{1290}(343, \cdot)\) 1290.2.m.a 4 2
1290.2.m.b 40
1290.2.m.c 44
1290.2.o \(\chi_{1290}(179, \cdot)\) n/a 176 2
1290.2.q \(\chi_{1290}(1211, \cdot)\) n/a 120 2
1290.2.t \(\chi_{1290}(49, \cdot)\) 1290.2.t.a 4 2
1290.2.t.b 4
1290.2.t.c 4
1290.2.t.d 4
1290.2.t.e 32
1290.2.t.f 40
1290.2.u \(\chi_{1290}(121, \cdot)\) n/a 192 6
1290.2.w \(\chi_{1290}(737, \cdot)\) n/a 352 4
1290.2.x \(\chi_{1290}(7, \cdot)\) n/a 176 4
1290.2.ba \(\chi_{1290}(379, \cdot)\) n/a 264 6
1290.2.bb \(\chi_{1290}(131, \cdot)\) n/a 336 6
1290.2.bf \(\chi_{1290}(389, \cdot)\) n/a 528 6
1290.2.bg \(\chi_{1290}(31, \cdot)\) n/a 336 12
1290.2.bh \(\chi_{1290}(217, \cdot)\) n/a 528 12
1290.2.bk \(\chi_{1290}(47, \cdot)\) n/a 1056 12
1290.2.bm \(\chi_{1290}(29, \cdot)\) n/a 1056 12
1290.2.bo \(\chi_{1290}(109, \cdot)\) n/a 528 12
1290.2.br \(\chi_{1290}(71, \cdot)\) n/a 720 12
1290.2.bt \(\chi_{1290}(73, \cdot)\) n/a 1056 24
1290.2.bu \(\chi_{1290}(17, \cdot)\) n/a 2112 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1290))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1290)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(258))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(430))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(645))\)\(^{\oplus 2}\)