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Properties

Label 2070.2
Level 2070
Weight 2
Dimension 27482
Nonzero newspaces 24
Sturm bound 456192
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(456192\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2070))\).

Total New Old
Modular forms 116864 27482 89382
Cusp forms 111233 27482 83751
Eisenstein series 5631 0 5631

Trace form

\( 27482 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 10 q^{5} + 12 q^{6} - 24 q^{7} + 6 q^{8} + 28 q^{9} + O(q^{10}) \) \( 27482 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 10 q^{5} + 12 q^{6} - 24 q^{7} + 6 q^{8} + 28 q^{9} + 22 q^{10} + 52 q^{11} + 16 q^{12} + 28 q^{13} + 40 q^{14} + 48 q^{15} - 6 q^{16} - 8 q^{17} + 8 q^{18} - 28 q^{19} + 72 q^{21} - 24 q^{22} - 52 q^{23} - 12 q^{24} - 10 q^{25} - 56 q^{26} + 48 q^{27} - 44 q^{28} - 32 q^{29} - 28 q^{31} - 6 q^{32} - 20 q^{33} - 8 q^{34} - 54 q^{35} - 20 q^{36} - 36 q^{37} - 84 q^{38} - 128 q^{39} + 6 q^{40} - 196 q^{41} - 128 q^{42} - 108 q^{43} - 64 q^{44} - 160 q^{45} - 208 q^{47} - 20 q^{48} - 138 q^{49} - 94 q^{50} - 60 q^{51} - 20 q^{52} - 104 q^{53} + 28 q^{54} + 128 q^{55} + 92 q^{56} + 212 q^{57} + 196 q^{58} + 464 q^{59} + 60 q^{60} + 500 q^{61} + 396 q^{62} + 520 q^{63} + 6 q^{64} + 546 q^{65} + 448 q^{66} + 300 q^{67} + 336 q^{68} + 504 q^{69} + 312 q^{70} + 804 q^{71} + 188 q^{72} + 380 q^{73} + 628 q^{74} + 296 q^{75} + 92 q^{76} + 684 q^{77} + 320 q^{78} + 548 q^{79} + 56 q^{80} + 348 q^{81} + 380 q^{82} + 280 q^{83} + 112 q^{84} + 170 q^{85} + 272 q^{86} + 40 q^{87} + 20 q^{88} + 48 q^{89} + 112 q^{90} + 40 q^{91} + 36 q^{92} - 64 q^{93} + 56 q^{94} - 2 q^{95} + 16 q^{96} + 176 q^{97} + 142 q^{98} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2070))\)

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
2070.2.a \(\chi_{2070}(1, \cdot)\) 2070.2.a.a 1 1
2070.2.a.b 1
2070.2.a.c 1
2070.2.a.d 1
2070.2.a.e 1
2070.2.a.f 1
2070.2.a.g 1
2070.2.a.h 1
2070.2.a.i 1
2070.2.a.j 1
2070.2.a.k 1
2070.2.a.l 1
2070.2.a.m 1
2070.2.a.n 1
2070.2.a.o 1
2070.2.a.p 1
2070.2.a.q 1
2070.2.a.r 1
2070.2.a.s 1
2070.2.a.t 2
2070.2.a.u 2
2070.2.a.v 2
2070.2.a.w 2
2070.2.a.x 2
2070.2.a.y 2
2070.2.a.z 3
2070.2.d \(\chi_{2070}(829, \cdot)\) 2070.2.d.a 4 1
2070.2.d.b 4
2070.2.d.c 4
2070.2.d.d 6
2070.2.d.e 6
2070.2.d.f 8
2070.2.d.g 8
2070.2.d.h 16
2070.2.e \(\chi_{2070}(1241, \cdot)\) 2070.2.e.a 16 1
2070.2.e.b 16
2070.2.h \(\chi_{2070}(2069, \cdot)\) 2070.2.h.a 24 1
2070.2.h.b 24
2070.2.i \(\chi_{2070}(691, \cdot)\) n/a 176 2
2070.2.j \(\chi_{2070}(323, \cdot)\) 2070.2.j.a 4 2
2070.2.j.b 4
2070.2.j.c 4
2070.2.j.d 4
2070.2.j.e 4
2070.2.j.f 4
2070.2.j.g 12
2070.2.j.h 16
2070.2.j.i 16
2070.2.j.j 20
2070.2.k \(\chi_{2070}(1333, \cdot)\) n/a 120 2
2070.2.n \(\chi_{2070}(689, \cdot)\) n/a 288 2
2070.2.q \(\chi_{2070}(551, \cdot)\) n/a 192 2
2070.2.r \(\chi_{2070}(139, \cdot)\) n/a 264 2
2070.2.u \(\chi_{2070}(271, \cdot)\) n/a 400 10
2070.2.x \(\chi_{2070}(47, \cdot)\) n/a 528 4
2070.2.y \(\chi_{2070}(367, \cdot)\) n/a 576 4
2070.2.z \(\chi_{2070}(89, \cdot)\) n/a 480 10
2070.2.bc \(\chi_{2070}(251, \cdot)\) n/a 320 10
2070.2.bd \(\chi_{2070}(289, \cdot)\) n/a 600 10
2070.2.bg \(\chi_{2070}(31, \cdot)\) n/a 1920 20
2070.2.bj \(\chi_{2070}(37, \cdot)\) n/a 1200 20
2070.2.bk \(\chi_{2070}(197, \cdot)\) n/a 960 20
2070.2.bn \(\chi_{2070}(49, \cdot)\) n/a 2880 20
2070.2.bo \(\chi_{2070}(11, \cdot)\) n/a 1920 20
2070.2.br \(\chi_{2070}(149, \cdot)\) n/a 2880 20
2070.2.bs \(\chi_{2070}(7, \cdot)\) n/a 5760 40
2070.2.bt \(\chi_{2070}(77, \cdot)\) n/a 5760 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2070))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2070)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1035))\)\(^{\oplus 2}\)