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Properties

Label 2010.2
Level 2010
Weight 2
Dimension 24669
Nonzero newspaces 24
Sturm bound 430848
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(430848\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2010))\).

Total New Old
Modular forms 109824 24669 85155
Cusp forms 105601 24669 80932
Eisenstein series 4223 0 4223

Trace form

\( 24669 q + q^{2} + 5 q^{3} + q^{4} + 9 q^{5} + 5 q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 24669 q + q^{2} + 5 q^{3} + q^{4} + 9 q^{5} + 5 q^{6} + 8 q^{7} + q^{8} + q^{9} - 7 q^{10} - 20 q^{11} - 11 q^{12} - 18 q^{13} - 24 q^{14} - 19 q^{15} + q^{16} - 30 q^{17} - 15 q^{18} - 12 q^{19} - 7 q^{20} - 8 q^{21} - 4 q^{22} - 24 q^{23} + 5 q^{24} + 17 q^{25} + 14 q^{26} + 5 q^{27} + 8 q^{28} - 18 q^{29} + 29 q^{30} + q^{32} - 4 q^{33} - 14 q^{34} - 24 q^{35} + q^{36} - 90 q^{37} - 28 q^{38} - 42 q^{39} - 23 q^{40} - 38 q^{41} - 24 q^{42} - 84 q^{43} - 4 q^{44} + 9 q^{45} - 72 q^{46} - 48 q^{47} - 11 q^{48} - 87 q^{49} - 15 q^{50} - 6 q^{51} + 70 q^{52} + 222 q^{53} + 5 q^{54} + 376 q^{55} - 8 q^{56} + 328 q^{57} + 526 q^{58} + 508 q^{59} + 145 q^{60} + 1054 q^{61} + 248 q^{62} + 52 q^{63} + q^{64} + 542 q^{65} + 492 q^{66} + 481 q^{67} + 234 q^{68} + 256 q^{69} + 536 q^{70} + 936 q^{71} + 17 q^{72} + 1106 q^{73} + 222 q^{74} + 221 q^{75} + 484 q^{76} + 432 q^{77} + 254 q^{78} + 520 q^{79} + 9 q^{80} - 63 q^{81} + 374 q^{82} + 156 q^{83} + 36 q^{84} - 30 q^{85} - 68 q^{86} - 58 q^{87} - 4 q^{88} - 166 q^{89} - 23 q^{90} - 144 q^{91} - 24 q^{92} - 64 q^{93} - 16 q^{94} - 28 q^{95} - 11 q^{96} - 126 q^{97} - 39 q^{98} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2010))\)

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
2010.2.a \(\chi_{2010}(1, \cdot)\) 2010.2.a.a 1 1
2010.2.a.b 1
2010.2.a.c 1
2010.2.a.d 1
2010.2.a.e 1
2010.2.a.f 1
2010.2.a.g 1
2010.2.a.h 1
2010.2.a.i 1
2010.2.a.j 1
2010.2.a.k 1
2010.2.a.l 2
2010.2.a.m 2
2010.2.a.n 3
2010.2.a.o 3
2010.2.a.p 3
2010.2.a.q 3
2010.2.a.r 4
2010.2.a.s 4
2010.2.a.t 5
2010.2.a.u 5
2010.2.d \(\chi_{2010}(401, \cdot)\) 2010.2.d.a 2 1
2010.2.d.b 2
2010.2.d.c 20
2010.2.d.d 20
2010.2.d.e 22
2010.2.d.f 22
2010.2.e \(\chi_{2010}(1609, \cdot)\) 2010.2.e.a 2 1
2010.2.e.b 2
2010.2.e.c 2
2010.2.e.d 2
2010.2.e.e 2
2010.2.e.f 2
2010.2.e.g 8
2010.2.e.h 10
2010.2.e.i 16
2010.2.e.j 18
2010.2.h \(\chi_{2010}(2009, \cdot)\) n/a 136 1
2010.2.i \(\chi_{2010}(841, \cdot)\) 2010.2.i.a 2 2
2010.2.i.b 10
2010.2.i.c 10
2010.2.i.d 10
2010.2.i.e 10
2010.2.i.f 10
2010.2.i.g 12
2010.2.i.h 12
2010.2.i.i 12
2010.2.j \(\chi_{2010}(133, \cdot)\) n/a 136 2
2010.2.k \(\chi_{2010}(1073, \cdot)\) n/a 264 2
2010.2.n \(\chi_{2010}(239, \cdot)\) n/a 272 2
2010.2.q \(\chi_{2010}(439, \cdot)\) n/a 136 2
2010.2.r \(\chi_{2010}(641, \cdot)\) n/a 184 2
2010.2.u \(\chi_{2010}(91, \cdot)\) n/a 480 10
2010.2.x \(\chi_{2010}(707, \cdot)\) n/a 544 4
2010.2.y \(\chi_{2010}(97, \cdot)\) n/a 272 4
2010.2.z \(\chi_{2010}(119, \cdot)\) n/a 1360 10
2010.2.bc \(\chi_{2010}(161, \cdot)\) n/a 880 10
2010.2.bd \(\chi_{2010}(349, \cdot)\) n/a 680 10
2010.2.bg \(\chi_{2010}(121, \cdot)\) n/a 880 20
2010.2.bj \(\chi_{2010}(43, \cdot)\) n/a 1360 20
2010.2.bk \(\chi_{2010}(107, \cdot)\) n/a 2720 20
2010.2.bn \(\chi_{2010}(19, \cdot)\) n/a 1360 20
2010.2.bo \(\chi_{2010}(11, \cdot)\) n/a 1840 20
2010.2.br \(\chi_{2010}(299, \cdot)\) n/a 2720 20
2010.2.bs \(\chi_{2010}(17, \cdot)\) n/a 5440 40
2010.2.bt \(\chi_{2010}(7, \cdot)\) n/a 2720 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2010))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(402))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(670))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1005))\)\(^{\oplus 2}\)