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Properties

Label 6030.2
Level 6030
Weight 2
Dimension 234392
Nonzero newspaces 60
Sturm bound 3877632

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Defining parameters

Level: \( N \) = \( 6030 = 2 \cdot 3^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(3877632\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6030))\).

Total New Old
Modular forms 977856 234392 743464
Cusp forms 960961 234392 726569
Eisenstein series 16895 0 16895

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6030))\)

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
6030.2.a \(\chi_{6030}(1, \cdot)\) 6030.2.a.a 1 1
6030.2.a.b 1
6030.2.a.c 1
6030.2.a.d 1
6030.2.a.e 1
6030.2.a.f 1
6030.2.a.g 1
6030.2.a.h 1
6030.2.a.i 1
6030.2.a.j 1
6030.2.a.k 1
6030.2.a.l 1
6030.2.a.m 1
6030.2.a.n 1
6030.2.a.o 1
6030.2.a.p 1
6030.2.a.q 1
6030.2.a.r 1
6030.2.a.s 1
6030.2.a.t 1
6030.2.a.u 1
6030.2.a.v 1
6030.2.a.w 1
6030.2.a.x 1
6030.2.a.y 1
6030.2.a.z 2
6030.2.a.ba 2
6030.2.a.bb 2
6030.2.a.bc 2
6030.2.a.bd 2
6030.2.a.be 2
6030.2.a.bf 2
6030.2.a.bg 2
6030.2.a.bh 2
6030.2.a.bi 2
6030.2.a.bj 3
6030.2.a.bk 3
6030.2.a.bl 3
6030.2.a.bm 3
6030.2.a.bn 3
6030.2.a.bo 3
6030.2.a.bp 3
6030.2.a.bq 3
6030.2.a.br 3
6030.2.a.bs 4
6030.2.a.bt 4
6030.2.a.bu 4
6030.2.a.bv 5
6030.2.a.bw 5
6030.2.a.bx 8
6030.2.a.by 8
6030.2.d \(\chi_{6030}(2411, \cdot)\) 6030.2.d.a 2 1
6030.2.d.b 2
6030.2.d.c 2
6030.2.d.d 2
6030.2.d.e 2
6030.2.d.f 2
6030.2.d.g 2
6030.2.d.h 2
6030.2.d.i 16
6030.2.d.j 16
6030.2.d.k 24
6030.2.d.l 24
6030.2.e \(\chi_{6030}(3619, \cdot)\) n/a 166 1
6030.2.h \(\chi_{6030}(6029, \cdot)\) n/a 136 1
6030.2.i \(\chi_{6030}(3781, \cdot)\) n/a 224 2
6030.2.j \(\chi_{6030}(2851, \cdot)\) n/a 544 2
6030.2.k \(\chi_{6030}(2011, \cdot)\) n/a 528 2
6030.2.l \(\chi_{6030}(841, \cdot)\) n/a 544 2
6030.2.m \(\chi_{6030}(937, \cdot)\) n/a 340 2
6030.2.n \(\chi_{6030}(3887, \cdot)\) n/a 264 2
6030.2.s \(\chi_{6030}(641, \cdot)\) n/a 544 2
6030.2.t \(\chi_{6030}(4459, \cdot)\) n/a 816 2
6030.2.u \(\chi_{6030}(239, \cdot)\) n/a 816 2
6030.2.v \(\chi_{6030}(1169, \cdot)\) n/a 272 2
6030.2.w \(\chi_{6030}(2009, \cdot)\) n/a 816 2
6030.2.bd \(\chi_{6030}(1609, \cdot)\) n/a 792 2
6030.2.be \(\chi_{6030}(401, \cdot)\) n/a 544 2
6030.2.bf \(\chi_{6030}(1369, \cdot)\) n/a 340 2
6030.2.bg \(\chi_{6030}(439, \cdot)\) n/a 816 2
6030.2.bh \(\chi_{6030}(2651, \cdot)\) n/a 544 2
6030.2.bi \(\chi_{6030}(3581, \cdot)\) n/a 176 2
6030.2.br \(\chi_{6030}(4259, \cdot)\) n/a 816 2
6030.2.bs \(\chi_{6030}(91, \cdot)\) n/a 1160 10
6030.2.bt \(\chi_{6030}(1177, \cdot)\) n/a 1632 4
6030.2.bu \(\chi_{6030}(707, \cdot)\) n/a 1632 4
6030.2.cb \(\chi_{6030}(1073, \cdot)\) n/a 1584 4
6030.2.cc \(\chi_{6030}(133, \cdot)\) n/a 1632 4
6030.2.cd \(\chi_{6030}(1637, \cdot)\) n/a 544 4
6030.2.ce \(\chi_{6030}(833, \cdot)\) n/a 1632 4
6030.2.cf \(\chi_{6030}(97, \cdot)\) n/a 1632 4
6030.2.cg \(\chi_{6030}(2107, \cdot)\) n/a 680 4
6030.2.cj \(\chi_{6030}(179, \cdot)\) n/a 1360 10
6030.2.cm \(\chi_{6030}(161, \cdot)\) n/a 960 10
6030.2.cn \(\chi_{6030}(829, \cdot)\) n/a 1700 10
6030.2.cq \(\chi_{6030}(121, \cdot)\) n/a 5440 20
6030.2.cr \(\chi_{6030}(241, \cdot)\) n/a 5440 20
6030.2.cs \(\chi_{6030}(151, \cdot)\) n/a 5440 20
6030.2.ct \(\chi_{6030}(181, \cdot)\) n/a 2240 20
6030.2.cw \(\chi_{6030}(253, \cdot)\) n/a 3400 20
6030.2.cx \(\chi_{6030}(107, \cdot)\) n/a 2720 20
6030.2.cy \(\chi_{6030}(299, \cdot)\) n/a 8160 20
6030.2.dh \(\chi_{6030}(619, \cdot)\) n/a 8160 20
6030.2.di \(\chi_{6030}(19, \cdot)\) n/a 3400 20
6030.2.dj \(\chi_{6030}(251, \cdot)\) n/a 1760 20
6030.2.dk \(\chi_{6030}(41, \cdot)\) n/a 5440 20
6030.2.dl \(\chi_{6030}(349, \cdot)\) n/a 8160 20
6030.2.dm \(\chi_{6030}(311, \cdot)\) n/a 5440 20
6030.2.dt \(\chi_{6030}(119, \cdot)\) n/a 8160 20
6030.2.du \(\chi_{6030}(899, \cdot)\) n/a 2720 20
6030.2.dv \(\chi_{6030}(599, \cdot)\) n/a 8160 20
6030.2.dw \(\chi_{6030}(11, \cdot)\) n/a 5440 20
6030.2.dx \(\chi_{6030}(49, \cdot)\) n/a 8160 20
6030.2.ec \(\chi_{6030}(83, \cdot)\) n/a 16320 40
6030.2.ed \(\chi_{6030}(17, \cdot)\) n/a 5440 40
6030.2.ee \(\chi_{6030}(433, \cdot)\) n/a 6800 40
6030.2.ef \(\chi_{6030}(247, \cdot)\) n/a 16320 40
6030.2.eg \(\chi_{6030}(263, \cdot)\) n/a 16320 40
6030.2.eh \(\chi_{6030}(43, \cdot)\) n/a 16320 40
6030.2.eo \(\chi_{6030}(7, \cdot)\) n/a 16320 40
6030.2.ep \(\chi_{6030}(23, \cdot)\) n/a 16320 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6030))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6030)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(402))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(603))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(670))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1005))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1206))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2010))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3015))\)\(^{\oplus 2}\)