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Properties

Label 5082.2
Level 5082
Weight 2
Dimension 164234
Nonzero newspaces 32
Sturm bound 2787840

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Defining parameters

Level: \( N \) = \( 5082 = 2 \cdot 3 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(2787840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5082))\).

Total New Old
Modular forms 704640 164234 540406
Cusp forms 689281 164234 525047
Eisenstein series 15359 0 15359

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5082))\)

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
5082.2.a \(\chi_{5082}(1, \cdot)\) 5082.2.a.a 1 1
5082.2.a.b 1
5082.2.a.c 1
5082.2.a.d 1
5082.2.a.e 1
5082.2.a.f 1
5082.2.a.g 1
5082.2.a.h 1
5082.2.a.i 1
5082.2.a.j 1
5082.2.a.k 1
5082.2.a.l 1
5082.2.a.m 1
5082.2.a.n 1
5082.2.a.o 1
5082.2.a.p 1
5082.2.a.q 1
5082.2.a.r 1
5082.2.a.s 1
5082.2.a.t 1
5082.2.a.u 1
5082.2.a.v 1
5082.2.a.w 1
5082.2.a.x 1
5082.2.a.y 1
5082.2.a.z 1
5082.2.a.ba 1
5082.2.a.bb 1
5082.2.a.bc 2
5082.2.a.bd 2
5082.2.a.be 2
5082.2.a.bf 2
5082.2.a.bg 2
5082.2.a.bh 2
5082.2.a.bi 2
5082.2.a.bj 2
5082.2.a.bk 2
5082.2.a.bl 2
5082.2.a.bm 2
5082.2.a.bn 2
5082.2.a.bo 2
5082.2.a.bp 2
5082.2.a.bq 2
5082.2.a.br 2
5082.2.a.bs 2
5082.2.a.bt 2
5082.2.a.bu 2
5082.2.a.bv 2
5082.2.a.bw 2
5082.2.a.bx 4
5082.2.a.by 4
5082.2.a.bz 4
5082.2.a.ca 4
5082.2.a.cb 4
5082.2.a.cc 4
5082.2.a.cd 4
5082.2.a.ce 4
5082.2.a.cf 4
5082.2.a.cg 4
5082.2.c \(\chi_{5082}(4355, \cdot)\) n/a 216 1
5082.2.e \(\chi_{5082}(1693, \cdot)\) n/a 144 1
5082.2.g \(\chi_{5082}(4115, \cdot)\) n/a 292 1
5082.2.i \(\chi_{5082}(1453, \cdot)\) n/a 292 2
5082.2.j \(\chi_{5082}(1219, \cdot)\) n/a 432 4
5082.2.k \(\chi_{5082}(1937, \cdot)\) n/a 580 2
5082.2.n \(\chi_{5082}(725, \cdot)\) n/a 576 2
5082.2.p \(\chi_{5082}(241, \cdot)\) n/a 288 2
5082.2.s \(\chi_{5082}(251, \cdot)\) n/a 1152 4
5082.2.u \(\chi_{5082}(475, \cdot)\) n/a 576 4
5082.2.w \(\chi_{5082}(239, \cdot)\) n/a 864 4
5082.2.y \(\chi_{5082}(463, \cdot)\) n/a 1320 10
5082.2.z \(\chi_{5082}(487, \cdot)\) n/a 1152 8
5082.2.bb \(\chi_{5082}(419, \cdot)\) n/a 3520 10
5082.2.bd \(\chi_{5082}(307, \cdot)\) n/a 1760 10
5082.2.bf \(\chi_{5082}(197, \cdot)\) n/a 2640 10
5082.2.bi \(\chi_{5082}(481, \cdot)\) n/a 1152 8
5082.2.bk \(\chi_{5082}(233, \cdot)\) n/a 2304 8
5082.2.bn \(\chi_{5082}(269, \cdot)\) n/a 2304 8
5082.2.bo \(\chi_{5082}(67, \cdot)\) n/a 3520 20
5082.2.bp \(\chi_{5082}(169, \cdot)\) n/a 5280 40
5082.2.br \(\chi_{5082}(439, \cdot)\) n/a 3520 20
5082.2.bt \(\chi_{5082}(65, \cdot)\) n/a 7040 20
5082.2.bw \(\chi_{5082}(89, \cdot)\) n/a 7040 20
5082.2.by \(\chi_{5082}(29, \cdot)\) n/a 10560 40
5082.2.ca \(\chi_{5082}(13, \cdot)\) n/a 7040 40
5082.2.cc \(\chi_{5082}(125, \cdot)\) n/a 14080 40
5082.2.ce \(\chi_{5082}(25, \cdot)\) n/a 14080 80
5082.2.cf \(\chi_{5082}(5, \cdot)\) n/a 28160 80
5082.2.ci \(\chi_{5082}(95, \cdot)\) n/a 28160 80
5082.2.ck \(\chi_{5082}(19, \cdot)\) n/a 14080 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5082))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5082)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1694))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2541))\)\(^{\oplus 2}\)