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Properties

Label 8050.2
Level 8050
Weight 2
Dimension 557520
Nonzero newspaces 48
Sturm bound 7603200

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Defining parameters

Level: \( N \) = \( 8050 = 2 \cdot 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(7603200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8050))\).

Total New Old
Modular forms 1915584 557520 1358064
Cusp forms 1886017 557520 1328497
Eisenstein series 29567 0 29567

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8050))\)

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
8050.2.a \(\chi_{8050}(1, \cdot)\) 8050.2.a.a 1 1
8050.2.a.b 1
8050.2.a.c 1
8050.2.a.d 1
8050.2.a.e 1
8050.2.a.f 1
8050.2.a.g 1
8050.2.a.h 1
8050.2.a.i 1
8050.2.a.j 1
8050.2.a.k 1
8050.2.a.l 1
8050.2.a.m 1
8050.2.a.n 1
8050.2.a.o 1
8050.2.a.p 1
8050.2.a.q 1
8050.2.a.r 1
8050.2.a.s 1
8050.2.a.t 1
8050.2.a.u 1
8050.2.a.v 2
8050.2.a.w 2
8050.2.a.x 2
8050.2.a.y 2
8050.2.a.z 2
8050.2.a.ba 2
8050.2.a.bb 2
8050.2.a.bc 2
8050.2.a.bd 2
8050.2.a.be 2
8050.2.a.bf 2
8050.2.a.bg 3
8050.2.a.bh 3
8050.2.a.bi 3
8050.2.a.bj 3
8050.2.a.bk 3
8050.2.a.bl 3
8050.2.a.bm 3
8050.2.a.bn 3
8050.2.a.bo 4
8050.2.a.bp 4
8050.2.a.bq 4
8050.2.a.br 5
8050.2.a.bs 5
8050.2.a.bt 5
8050.2.a.bu 5
8050.2.a.bv 5
8050.2.a.bw 5
8050.2.a.bx 5
8050.2.a.by 6
8050.2.a.bz 6
8050.2.a.ca 7
8050.2.a.cb 7
8050.2.a.cc 7
8050.2.a.cd 7
8050.2.a.ce 7
8050.2.a.cf 7
8050.2.a.cg 9
8050.2.a.ch 9
8050.2.a.ci 11
8050.2.a.cj 11
8050.2.c \(\chi_{8050}(5151, \cdot)\) n/a 304 1
8050.2.e \(\chi_{8050}(2899, \cdot)\) n/a 200 1
8050.2.g \(\chi_{8050}(8049, \cdot)\) n/a 288 1
8050.2.i \(\chi_{8050}(4601, \cdot)\) n/a 560 2
8050.2.k \(\chi_{8050}(1793, \cdot)\) n/a 432 2
8050.2.m \(\chi_{8050}(2393, \cdot)\) n/a 528 2
8050.2.n \(\chi_{8050}(1611, \cdot)\) n/a 1328 4
8050.2.p \(\chi_{8050}(2299, \cdot)\) n/a 576 2
8050.2.r \(\chi_{8050}(599, \cdot)\) n/a 528 2
8050.2.t \(\chi_{8050}(551, \cdot)\) n/a 608 2
8050.2.w \(\chi_{8050}(1609, \cdot)\) n/a 1920 4
8050.2.y \(\chi_{8050}(1289, \cdot)\) n/a 1312 4
8050.2.ba \(\chi_{8050}(321, \cdot)\) n/a 1920 4
8050.2.bc \(\chi_{8050}(351, \cdot)\) n/a 2280 10
8050.2.bd \(\chi_{8050}(507, \cdot)\) n/a 1056 4
8050.2.bf \(\chi_{8050}(2207, \cdot)\) n/a 1152 4
8050.2.bh \(\chi_{8050}(921, \cdot)\) n/a 3520 8
8050.2.bi \(\chi_{8050}(783, \cdot)\) n/a 3520 8
8050.2.bk \(\chi_{8050}(183, \cdot)\) n/a 2880 8
8050.2.bn \(\chi_{8050}(1049, \cdot)\) n/a 2880 10
8050.2.bp \(\chi_{8050}(449, \cdot)\) n/a 2160 10
8050.2.br \(\chi_{8050}(251, \cdot)\) n/a 3040 10
8050.2.bu \(\chi_{8050}(1011, \cdot)\) n/a 3840 8
8050.2.bw \(\chi_{8050}(1059, \cdot)\) n/a 3520 8
8050.2.by \(\chi_{8050}(229, \cdot)\) n/a 3840 8
8050.2.ca \(\chi_{8050}(151, \cdot)\) n/a 6080 20
8050.2.cb \(\chi_{8050}(307, \cdot)\) n/a 5760 20
8050.2.cd \(\chi_{8050}(43, \cdot)\) n/a 4320 20
8050.2.cf \(\chi_{8050}(71, \cdot)\) n/a 14400 40
8050.2.ch \(\chi_{8050}(137, \cdot)\) n/a 7680 16
8050.2.cj \(\chi_{8050}(47, \cdot)\) n/a 7040 16
8050.2.cl \(\chi_{8050}(201, \cdot)\) n/a 6080 20
8050.2.cn \(\chi_{8050}(499, \cdot)\) n/a 5760 20
8050.2.cp \(\chi_{8050}(199, \cdot)\) n/a 5760 20
8050.2.cs \(\chi_{8050}(111, \cdot)\) n/a 19200 40
8050.2.cu \(\chi_{8050}(29, \cdot)\) n/a 14400 40
8050.2.cw \(\chi_{8050}(419, \cdot)\) n/a 19200 40
8050.2.cz \(\chi_{8050}(107, \cdot)\) n/a 11520 40
8050.2.db \(\chi_{8050}(243, \cdot)\) n/a 11520 40
8050.2.dc \(\chi_{8050}(81, \cdot)\) n/a 38400 80
8050.2.de \(\chi_{8050}(113, \cdot)\) n/a 28800 80
8050.2.dg \(\chi_{8050}(13, \cdot)\) n/a 38400 80
8050.2.di \(\chi_{8050}(19, \cdot)\) n/a 38400 80
8050.2.dk \(\chi_{8050}(9, \cdot)\) n/a 38400 80
8050.2.dm \(\chi_{8050}(61, \cdot)\) n/a 38400 80
8050.2.do \(\chi_{8050}(3, \cdot)\) n/a 76800 160
8050.2.dq \(\chi_{8050}(37, \cdot)\) n/a 76800 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8050))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8050)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(805))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1610))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4025))\)\(^{\oplus 2}\)