Properties

Label 2070.4
Level 2070
Weight 4
Dimension 82450
Nonzero newspaces 24
Sturm bound 912384
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(912384\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2070))\).

Total New Old
Modular forms 344960 82450 262510
Cusp forms 339328 82450 256878
Eisenstein series 5632 0 5632

Trace form

\( 82450 q + 12 q^{2} + 12 q^{3} - 24 q^{4} + 34 q^{5} - 72 q^{6} - 8 q^{7} - 48 q^{8} - 164 q^{9} + 68 q^{10} + 68 q^{11} - 32 q^{12} - 596 q^{13} - 400 q^{14} - 492 q^{15} - 224 q^{16} - 1060 q^{17} + 560 q^{18}+ \cdots - 5024 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2070))\)

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
2070.4.a \(\chi_{2070}(1, \cdot)\) 2070.4.a.a 1 1
2070.4.a.b 1
2070.4.a.c 1
2070.4.a.d 1
2070.4.a.e 1
2070.4.a.f 1
2070.4.a.g 1
2070.4.a.h 1
2070.4.a.i 1
2070.4.a.j 1
2070.4.a.k 1
2070.4.a.l 1
2070.4.a.m 1
2070.4.a.n 1
2070.4.a.o 1
2070.4.a.p 2
2070.4.a.q 2
2070.4.a.r 2
2070.4.a.s 2
2070.4.a.t 2
2070.4.a.u 3
2070.4.a.v 3
2070.4.a.w 3
2070.4.a.x 3
2070.4.a.y 3
2070.4.a.z 3
2070.4.a.ba 3
2070.4.a.bb 3
2070.4.a.bc 3
2070.4.a.bd 3
2070.4.a.be 3
2070.4.a.bf 4
2070.4.a.bg 4
2070.4.a.bh 4
2070.4.a.bi 4
2070.4.a.bj 4
2070.4.a.bk 5
2070.4.a.bl 5
2070.4.a.bm 5
2070.4.a.bn 5
2070.4.a.bo 6
2070.4.a.bp 6
2070.4.d \(\chi_{2070}(829, \cdot)\) n/a 164 1
2070.4.e \(\chi_{2070}(1241, \cdot)\) 2070.4.e.a 48 1
2070.4.e.b 48
2070.4.h \(\chi_{2070}(2069, \cdot)\) n/a 144 1
2070.4.i \(\chi_{2070}(691, \cdot)\) n/a 528 2
2070.4.j \(\chi_{2070}(323, \cdot)\) n/a 264 2
2070.4.k \(\chi_{2070}(1333, \cdot)\) n/a 360 2
2070.4.n \(\chi_{2070}(689, \cdot)\) n/a 864 2
2070.4.q \(\chi_{2070}(551, \cdot)\) n/a 576 2
2070.4.r \(\chi_{2070}(139, \cdot)\) n/a 792 2
2070.4.u \(\chi_{2070}(271, \cdot)\) n/a 1200 10
2070.4.x \(\chi_{2070}(47, \cdot)\) n/a 1584 4
2070.4.y \(\chi_{2070}(367, \cdot)\) n/a 1728 4
2070.4.z \(\chi_{2070}(89, \cdot)\) n/a 1440 10
2070.4.bc \(\chi_{2070}(251, \cdot)\) n/a 960 10
2070.4.bd \(\chi_{2070}(289, \cdot)\) n/a 1800 10
2070.4.bg \(\chi_{2070}(31, \cdot)\) n/a 5760 20
2070.4.bj \(\chi_{2070}(37, \cdot)\) n/a 3600 20
2070.4.bk \(\chi_{2070}(197, \cdot)\) n/a 2880 20
2070.4.bn \(\chi_{2070}(49, \cdot)\) n/a 8640 20
2070.4.bo \(\chi_{2070}(11, \cdot)\) n/a 5760 20
2070.4.br \(\chi_{2070}(149, \cdot)\) n/a 8640 20
2070.4.bs \(\chi_{2070}(7, \cdot)\) n/a 17280 40
2070.4.bt \(\chi_{2070}(77, \cdot)\) n/a 17280 40

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2070))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2070)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1035))\)\(^{\oplus 2}\)