Properties

Label 4830.2
Level 4830
Weight 2
Dimension 133087
Nonzero newspaces 48
Sturm bound 2433024

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Defining parameters

Level: \( N \) = \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(2433024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4830))\).

Total New Old
Modular forms 616704 133087 483617
Cusp forms 599809 133087 466722
Eisenstein series 16895 0 16895

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4830))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4830.2.a \(\chi_{4830}(1, \cdot)\) 4830.2.a.a 1 1
4830.2.a.b 1
4830.2.a.c 1
4830.2.a.d 1
4830.2.a.e 1
4830.2.a.f 1
4830.2.a.g 1
4830.2.a.h 1
4830.2.a.i 1
4830.2.a.j 1
4830.2.a.k 1
4830.2.a.l 1
4830.2.a.m 1
4830.2.a.n 1
4830.2.a.o 1
4830.2.a.p 1
4830.2.a.q 1
4830.2.a.r 1
4830.2.a.s 1
4830.2.a.t 1
4830.2.a.u 1
4830.2.a.v 1
4830.2.a.w 1
4830.2.a.x 1
4830.2.a.y 1
4830.2.a.z 1
4830.2.a.ba 1
4830.2.a.bb 1
4830.2.a.bc 1
4830.2.a.bd 1
4830.2.a.be 1
4830.2.a.bf 1
4830.2.a.bg 1
4830.2.a.bh 1
4830.2.a.bi 1
4830.2.a.bj 1
4830.2.a.bk 1
4830.2.a.bl 1
4830.2.a.bm 2
4830.2.a.bn 2
4830.2.a.bo 2
4830.2.a.bp 2
4830.2.a.bq 2
4830.2.a.br 2
4830.2.a.bs 2
4830.2.a.bt 2
4830.2.a.bu 2
4830.2.a.bv 2
4830.2.a.bw 3
4830.2.a.bx 3
4830.2.a.by 3
4830.2.a.bz 3
4830.2.a.ca 3
4830.2.a.cb 3
4830.2.a.cc 3
4830.2.a.cd 4
4830.2.a.ce 4
4830.2.b \(\chi_{4830}(461, \cdot)\) n/a 240 1
4830.2.e \(\chi_{4830}(3541, \cdot)\) n/a 128 1
4830.2.f \(\chi_{4830}(3359, \cdot)\) n/a 352 1
4830.2.i \(\chi_{4830}(1609, \cdot)\) n/a 192 1
4830.2.j \(\chi_{4830}(2759, \cdot)\) n/a 288 1
4830.2.m \(\chi_{4830}(2899, \cdot)\) n/a 136 1
4830.2.n \(\chi_{4830}(4691, \cdot)\) n/a 192 1
4830.2.q \(\chi_{4830}(1381, \cdot)\) n/a 240 2
4830.2.s \(\chi_{4830}(323, \cdot)\) n/a 528 2
4830.2.t \(\chi_{4830}(2437, \cdot)\) n/a 288 2
4830.2.w \(\chi_{4830}(2897, \cdot)\) n/a 768 2
4830.2.x \(\chi_{4830}(3037, \cdot)\) n/a 352 2
4830.2.ba \(\chi_{4830}(2209, \cdot)\) n/a 352 2
4830.2.bb \(\chi_{4830}(2069, \cdot)\) n/a 768 2
4830.2.be \(\chi_{4830}(1241, \cdot)\) n/a 512 2
4830.2.bh \(\chi_{4830}(2161, \cdot)\) n/a 256 2
4830.2.bi \(\chi_{4830}(1151, \cdot)\) n/a 464 2
4830.2.bl \(\chi_{4830}(229, \cdot)\) n/a 384 2
4830.2.bm \(\chi_{4830}(1979, \cdot)\) n/a 704 2
4830.2.bo \(\chi_{4830}(211, \cdot)\) n/a 960 10
4830.2.bp \(\chi_{4830}(1657, \cdot)\) n/a 704 4
4830.2.bs \(\chi_{4830}(1517, \cdot)\) n/a 1536 4
4830.2.bt \(\chi_{4830}(1747, \cdot)\) n/a 768 4
4830.2.bw \(\chi_{4830}(737, \cdot)\) n/a 1408 4
4830.2.bz \(\chi_{4830}(281, \cdot)\) n/a 1920 10
4830.2.ca \(\chi_{4830}(169, \cdot)\) n/a 1440 10
4830.2.cd \(\chi_{4830}(659, \cdot)\) n/a 2880 10
4830.2.ce \(\chi_{4830}(559, \cdot)\) n/a 1920 10
4830.2.ch \(\chi_{4830}(209, \cdot)\) n/a 3840 10
4830.2.ci \(\chi_{4830}(181, \cdot)\) n/a 1280 10
4830.2.cl \(\chi_{4830}(41, \cdot)\) n/a 2560 10
4830.2.cm \(\chi_{4830}(121, \cdot)\) n/a 2560 20
4830.2.co \(\chi_{4830}(13, \cdot)\) n/a 3840 20
4830.2.cp \(\chi_{4830}(83, \cdot)\) n/a 7680 20
4830.2.cs \(\chi_{4830}(43, \cdot)\) n/a 2880 20
4830.2.ct \(\chi_{4830}(197, \cdot)\) n/a 5760 20
4830.2.cw \(\chi_{4830}(59, \cdot)\) n/a 7680 20
4830.2.cx \(\chi_{4830}(19, \cdot)\) n/a 3840 20
4830.2.da \(\chi_{4830}(101, \cdot)\) n/a 5120 20
4830.2.db \(\chi_{4830}(61, \cdot)\) n/a 2560 20
4830.2.de \(\chi_{4830}(11, \cdot)\) n/a 5120 20
4830.2.dh \(\chi_{4830}(149, \cdot)\) n/a 7680 20
4830.2.di \(\chi_{4830}(289, \cdot)\) n/a 3840 20
4830.2.dk \(\chi_{4830}(233, \cdot)\) n/a 15360 40
4830.2.dn \(\chi_{4830}(37, \cdot)\) n/a 7680 40
4830.2.do \(\chi_{4830}(17, \cdot)\) n/a 15360 40
4830.2.dr \(\chi_{4830}(73, \cdot)\) n/a 7680 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4830))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4830)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(805))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(966))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1610))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2415))\)\(^{\oplus 2}\)