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Properties

Label 2890.2
Level 2890
Weight 2
Dimension 75767
Nonzero newspaces 20
Sturm bound 998784
Trace bound 10

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Defining parameters

Level: \( N \) = \( 2890 = 2 \cdot 5 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(998784\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2890))\).

Total New Old
Modular forms 252896 75767 177129
Cusp forms 246497 75767 170730
Eisenstein series 6399 0 6399

Trace form

\( 75767 q - q^{2} - 4 q^{3} - q^{4} - q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 75767 q - q^{2} - 4 q^{3} - q^{4} - q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + 7 q^{10} + 52 q^{11} + 28 q^{12} + 50 q^{13} + 56 q^{14} + 92 q^{15} + 15 q^{16} + 32 q^{17} + 115 q^{18} + 44 q^{19} + 7 q^{20} + 160 q^{21} + 52 q^{22} + 40 q^{23} + 28 q^{24} + 71 q^{25} + 2 q^{26} + 56 q^{27} - 8 q^{28} + 50 q^{29} - 4 q^{30} + 96 q^{31} - q^{32} + 80 q^{33} + 56 q^{35} - 13 q^{36} + 90 q^{37} + 12 q^{38} + 200 q^{39} - q^{40} + 230 q^{41} + 160 q^{42} + 180 q^{43} + 116 q^{44} + 155 q^{45} + 104 q^{46} + 272 q^{47} - 4 q^{48} + 199 q^{49} + 31 q^{50} + 128 q^{51} + 114 q^{52} + 218 q^{53} + 184 q^{54} + 148 q^{55} - 8 q^{56} + 272 q^{57} + 98 q^{58} + 260 q^{59} + 60 q^{60} + 130 q^{61} + 160 q^{62} + 280 q^{63} - q^{64} + 58 q^{65} - 16 q^{66} - 4 q^{67} - 8 q^{68} - 96 q^{69} - 200 q^{70} - 136 q^{71} - 93 q^{72} - 378 q^{73} - 182 q^{74} - 292 q^{75} - 20 q^{76} - 288 q^{77} - 312 q^{78} - 272 q^{79} - 97 q^{80} - 473 q^{81} - 314 q^{82} - 180 q^{83} - 160 q^{84} - 252 q^{85} - 172 q^{86} - 312 q^{87} - 140 q^{88} - 90 q^{89} - 421 q^{90} - 240 q^{91} - 88 q^{92} - 128 q^{93} - 304 q^{94} - 244 q^{95} - 4 q^{96} - 226 q^{97} - 201 q^{98} - 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2890))\)

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
2890.2.a \(\chi_{2890}(1, \cdot)\) 2890.2.a.a 1 1
2890.2.a.b 1
2890.2.a.c 1
2890.2.a.d 1
2890.2.a.e 1
2890.2.a.f 1
2890.2.a.g 1
2890.2.a.h 1
2890.2.a.i 1
2890.2.a.j 1
2890.2.a.k 1
2890.2.a.l 1
2890.2.a.m 1
2890.2.a.n 1
2890.2.a.o 1
2890.2.a.p 1
2890.2.a.q 1
2890.2.a.r 2
2890.2.a.s 2
2890.2.a.t 2
2890.2.a.u 2
2890.2.a.v 2
2890.2.a.w 3
2890.2.a.x 3
2890.2.a.y 3
2890.2.a.z 3
2890.2.a.ba 3
2890.2.a.bb 3
2890.2.a.bc 4
2890.2.a.bd 4
2890.2.a.be 4
2890.2.a.bf 4
2890.2.a.bg 6
2890.2.a.bh 6
2890.2.a.bi 8
2890.2.a.bj 8
2890.2.b \(\chi_{2890}(2311, \cdot)\) 2890.2.b.a 2 1
2890.2.b.b 2
2890.2.b.c 2
2890.2.b.d 2
2890.2.b.e 2
2890.2.b.f 2
2890.2.b.g 2
2890.2.b.h 2
2890.2.b.i 4
2890.2.b.j 4
2890.2.b.k 4
2890.2.b.l 6
2890.2.b.m 6
2890.2.b.n 6
2890.2.b.o 8
2890.2.b.p 8
2890.2.b.q 12
2890.2.b.r 16
2890.2.c \(\chi_{2890}(579, \cdot)\) n/a 136 1
2890.2.d \(\chi_{2890}(2889, \cdot)\) n/a 136 1
2890.2.g \(\chi_{2890}(829, \cdot)\) n/a 272 2
2890.2.h \(\chi_{2890}(251, \cdot)\) n/a 180 2
2890.2.k \(\chi_{2890}(1001, \cdot)\) n/a 360 4
2890.2.n \(\chi_{2890}(179, \cdot)\) n/a 536 4
2890.2.o \(\chi_{2890}(513, \cdot)\) n/a 1080 8
2890.2.r \(\chi_{2890}(447, \cdot)\) n/a 1080 8
2890.2.s \(\chi_{2890}(171, \cdot)\) n/a 1632 16
2890.2.t \(\chi_{2890}(169, \cdot)\) n/a 2432 16
2890.2.u \(\chi_{2890}(69, \cdot)\) n/a 2432 16
2890.2.v \(\chi_{2890}(101, \cdot)\) n/a 1632 16
2890.2.y \(\chi_{2890}(21, \cdot)\) n/a 3264 32
2890.2.z \(\chi_{2890}(89, \cdot)\) n/a 4864 32
2890.2.bc \(\chi_{2890}(9, \cdot)\) n/a 9856 64
2890.2.bf \(\chi_{2890}(111, \cdot)\) n/a 6528 64
2890.2.bg \(\chi_{2890}(23, \cdot)\) n/a 19584 128
2890.2.bj \(\chi_{2890}(3, \cdot)\) n/a 19584 128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2890))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2890)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1445))\)\(^{\oplus 2}\)