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Properties

Label 5070.2
Level 5070
Weight 2
Dimension 154316
Nonzero newspaces 40
Sturm bound 2725632

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Defining parameters

Level: \( N \) = \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(2725632\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5070))\).

Total New Old
Modular forms 688704 154316 534388
Cusp forms 674113 154316 519797
Eisenstein series 14591 0 14591

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5070))\)

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
5070.2.a \(\chi_{5070}(1, \cdot)\) 5070.2.a.a 1 1
5070.2.a.b 1
5070.2.a.c 1
5070.2.a.d 1
5070.2.a.e 1
5070.2.a.f 1
5070.2.a.g 1
5070.2.a.h 1
5070.2.a.i 1
5070.2.a.j 1
5070.2.a.k 1
5070.2.a.l 1
5070.2.a.m 1
5070.2.a.n 1
5070.2.a.o 1
5070.2.a.p 1
5070.2.a.q 1
5070.2.a.r 1
5070.2.a.s 1
5070.2.a.t 1
5070.2.a.u 1
5070.2.a.v 1
5070.2.a.w 1
5070.2.a.x 1
5070.2.a.y 2
5070.2.a.z 2
5070.2.a.ba 2
5070.2.a.bb 2
5070.2.a.bc 2
5070.2.a.bd 2
5070.2.a.be 2
5070.2.a.bf 2
5070.2.a.bg 2
5070.2.a.bh 2
5070.2.a.bi 2
5070.2.a.bj 3
5070.2.a.bk 3
5070.2.a.bl 3
5070.2.a.bm 3
5070.2.a.bn 3
5070.2.a.bo 3
5070.2.a.bp 3
5070.2.a.bq 3
5070.2.a.br 3
5070.2.a.bs 3
5070.2.a.bt 3
5070.2.a.bu 3
5070.2.a.bv 3
5070.2.a.bw 3
5070.2.a.bx 3
5070.2.a.by 3
5070.2.a.bz 4
5070.2.a.ca 4
5070.2.b \(\chi_{5070}(1351, \cdot)\) 5070.2.b.a 2 1
5070.2.b.b 2
5070.2.b.c 2
5070.2.b.d 2
5070.2.b.e 2
5070.2.b.f 2
5070.2.b.g 2
5070.2.b.h 2
5070.2.b.i 2
5070.2.b.j 2
5070.2.b.k 2
5070.2.b.l 2
5070.2.b.m 2
5070.2.b.n 2
5070.2.b.o 4
5070.2.b.p 4
5070.2.b.q 4
5070.2.b.r 4
5070.2.b.s 6
5070.2.b.t 6
5070.2.b.u 6
5070.2.b.v 6
5070.2.b.w 6
5070.2.b.x 6
5070.2.b.y 6
5070.2.b.z 6
5070.2.b.ba 8
5070.2.e \(\chi_{5070}(2029, \cdot)\) n/a 154 1
5070.2.f \(\chi_{5070}(3379, \cdot)\) n/a 156 1
5070.2.i \(\chi_{5070}(991, \cdot)\) n/a 208 2
5070.2.j \(\chi_{5070}(577, \cdot)\) n/a 308 2
5070.2.l \(\chi_{5070}(677, \cdot)\) n/a 620 2
5070.2.n \(\chi_{5070}(239, \cdot)\) n/a 616 2
5070.2.p \(\chi_{5070}(1451, \cdot)\) n/a 416 2
5070.2.s \(\chi_{5070}(1013, \cdot)\) n/a 616 2
5070.2.t \(\chi_{5070}(3817, \cdot)\) n/a 308 2
5070.2.x \(\chi_{5070}(2389, \cdot)\) n/a 312 2
5070.2.y \(\chi_{5070}(529, \cdot)\) n/a 304 2
5070.2.bb \(\chi_{5070}(361, \cdot)\) n/a 208 2
5070.2.bd \(\chi_{5070}(427, \cdot)\) n/a 616 4
5070.2.be \(\chi_{5070}(23, \cdot)\) n/a 1232 4
5070.2.bh \(\chi_{5070}(1601, \cdot)\) n/a 816 4
5070.2.bj \(\chi_{5070}(89, \cdot)\) n/a 1232 4
5070.2.bl \(\chi_{5070}(653, \cdot)\) n/a 1232 4
5070.2.bn \(\chi_{5070}(1333, \cdot)\) n/a 616 4
5070.2.bo \(\chi_{5070}(391, \cdot)\) n/a 1488 12
5070.2.bq \(\chi_{5070}(259, \cdot)\) n/a 2160 12
5070.2.bt \(\chi_{5070}(79, \cdot)\) n/a 2208 12
5070.2.bu \(\chi_{5070}(181, \cdot)\) n/a 1488 12
5070.2.bw \(\chi_{5070}(61, \cdot)\) n/a 2880 24
5070.2.by \(\chi_{5070}(307, \cdot)\) n/a 4368 24
5070.2.ca \(\chi_{5070}(77, \cdot)\) n/a 8736 24
5070.2.cc \(\chi_{5070}(161, \cdot)\) n/a 5760 24
5070.2.ce \(\chi_{5070}(359, \cdot)\) n/a 8736 24
5070.2.cf \(\chi_{5070}(53, \cdot)\) n/a 8736 24
5070.2.ci \(\chi_{5070}(73, \cdot)\) n/a 4368 24
5070.2.ck \(\chi_{5070}(121, \cdot)\) n/a 2880 24
5070.2.cl \(\chi_{5070}(139, \cdot)\) n/a 4416 24
5070.2.co \(\chi_{5070}(49, \cdot)\) n/a 4320 24
5070.2.cq \(\chi_{5070}(67, \cdot)\) n/a 8736 48
5070.2.ct \(\chi_{5070}(107, \cdot)\) n/a 17472 48
5070.2.cu \(\chi_{5070}(59, \cdot)\) n/a 17472 48
5070.2.cw \(\chi_{5070}(11, \cdot)\) n/a 11712 48
5070.2.cy \(\chi_{5070}(17, \cdot)\) n/a 17472 48
5070.2.da \(\chi_{5070}(7, \cdot)\) n/a 8736 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5070))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5070)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2535))\)\(^{\oplus 2}\)