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Properties

Label 6624.2
Level 6624
Weight 2
Dimension 537786
Nonzero newspaces 48
Sturm bound 4866048

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Defining parameters

Level: \( N \) = \( 6624 = 2^{5} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(4866048\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6624))\).

Total New Old
Modular forms 1227776 541566 686210
Cusp forms 1205249 537786 667463
Eisenstein series 22527 3780 18747

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6624))\)

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
6624.2.a \(\chi_{6624}(1, \cdot)\) 6624.2.a.a 1 1
6624.2.a.b 1
6624.2.a.c 1
6624.2.a.d 1
6624.2.a.e 1
6624.2.a.f 1
6624.2.a.g 1
6624.2.a.h 1
6624.2.a.i 1
6624.2.a.j 1
6624.2.a.k 2
6624.2.a.l 2
6624.2.a.m 2
6624.2.a.n 2
6624.2.a.o 2
6624.2.a.p 2
6624.2.a.q 2
6624.2.a.r 2
6624.2.a.s 2
6624.2.a.t 2
6624.2.a.u 3
6624.2.a.v 3
6624.2.a.w 3
6624.2.a.x 3
6624.2.a.y 3
6624.2.a.z 3
6624.2.a.ba 3
6624.2.a.bb 3
6624.2.a.bc 3
6624.2.a.bd 3
6624.2.a.be 4
6624.2.a.bf 4
6624.2.a.bg 4
6624.2.a.bh 4
6624.2.a.bi 4
6624.2.a.bj 4
6624.2.a.bk 5
6624.2.a.bl 5
6624.2.a.bm 8
6624.2.a.bn 8
6624.2.b \(\chi_{6624}(2897, \cdot)\) 6624.2.b.a 8 1
6624.2.b.b 8
6624.2.b.c 80
6624.2.e \(\chi_{6624}(1151, \cdot)\) 6624.2.e.a 20 1
6624.2.e.b 20
6624.2.e.c 24
6624.2.e.d 24
6624.2.f \(\chi_{6624}(3313, \cdot)\) n/a 110 1
6624.2.i \(\chi_{6624}(5887, \cdot)\) n/a 120 1
6624.2.j \(\chi_{6624}(4463, \cdot)\) 6624.2.j.a 44 1
6624.2.j.b 44
6624.2.m \(\chi_{6624}(6209, \cdot)\) 6624.2.m.a 48 1
6624.2.m.b 48
6624.2.n \(\chi_{6624}(2575, \cdot)\) n/a 118 1
6624.2.q \(\chi_{6624}(2209, \cdot)\) n/a 528 2
6624.2.r \(\chi_{6624}(919, \cdot)\) None 0 2
6624.2.u \(\chi_{6624}(1657, \cdot)\) None 0 2
6624.2.v \(\chi_{6624}(2807, \cdot)\) None 0 2
6624.2.y \(\chi_{6624}(1241, \cdot)\) None 0 2
6624.2.bb \(\chi_{6624}(367, \cdot)\) n/a 568 2
6624.2.bc \(\chi_{6624}(1793, \cdot)\) n/a 576 2
6624.2.bf \(\chi_{6624}(47, \cdot)\) n/a 528 2
6624.2.bg \(\chi_{6624}(1471, \cdot)\) n/a 576 2
6624.2.bj \(\chi_{6624}(1105, \cdot)\) n/a 528 2
6624.2.bk \(\chi_{6624}(3359, \cdot)\) n/a 528 2
6624.2.bn \(\chi_{6624}(689, \cdot)\) n/a 568 2
6624.2.bq \(\chi_{6624}(829, \cdot)\) n/a 1760 4
6624.2.br \(\chi_{6624}(413, \cdot)\) n/a 1536 4
6624.2.bs \(\chi_{6624}(323, \cdot)\) n/a 1408 4
6624.2.bt \(\chi_{6624}(91, \cdot)\) n/a 1912 4
6624.2.bw \(\chi_{6624}(289, \cdot)\) n/a 1200 10
6624.2.by \(\chi_{6624}(599, \cdot)\) None 0 4
6624.2.bz \(\chi_{6624}(137, \cdot)\) None 0 4
6624.2.cc \(\chi_{6624}(2023, \cdot)\) None 0 4
6624.2.cd \(\chi_{6624}(553, \cdot)\) None 0 4
6624.2.ch \(\chi_{6624}(559, \cdot)\) n/a 1180 10
6624.2.ci \(\chi_{6624}(1601, \cdot)\) n/a 960 10
6624.2.cl \(\chi_{6624}(719, \cdot)\) n/a 960 10
6624.2.cm \(\chi_{6624}(1279, \cdot)\) n/a 1200 10
6624.2.cp \(\chi_{6624}(721, \cdot)\) n/a 1180 10
6624.2.cq \(\chi_{6624}(863, \cdot)\) n/a 960 10
6624.2.ct \(\chi_{6624}(17, \cdot)\) n/a 960 10
6624.2.cu \(\chi_{6624}(965, \cdot)\) n/a 9184 8
6624.2.cv \(\chi_{6624}(277, \cdot)\) n/a 8448 8
6624.2.da \(\chi_{6624}(643, \cdot)\) n/a 9184 8
6624.2.db \(\chi_{6624}(875, \cdot)\) n/a 8448 8
6624.2.dc \(\chi_{6624}(193, \cdot)\) n/a 5760 20
6624.2.dd \(\chi_{6624}(89, \cdot)\) None 0 20
6624.2.dg \(\chi_{6624}(71, \cdot)\) None 0 20
6624.2.dh \(\chi_{6624}(73, \cdot)\) None 0 20
6624.2.dk \(\chi_{6624}(199, \cdot)\) None 0 20
6624.2.dl \(\chi_{6624}(113, \cdot)\) n/a 5680 20
6624.2.do \(\chi_{6624}(95, \cdot)\) n/a 5760 20
6624.2.dp \(\chi_{6624}(49, \cdot)\) n/a 5680 20
6624.2.ds \(\chi_{6624}(319, \cdot)\) n/a 5760 20
6624.2.dt \(\chi_{6624}(239, \cdot)\) n/a 5680 20
6624.2.dw \(\chi_{6624}(65, \cdot)\) n/a 5760 20
6624.2.dx \(\chi_{6624}(79, \cdot)\) n/a 5680 20
6624.2.ec \(\chi_{6624}(35, \cdot)\) n/a 15360 40
6624.2.ed \(\chi_{6624}(19, \cdot)\) n/a 19120 40
6624.2.ee \(\chi_{6624}(325, \cdot)\) n/a 19120 40
6624.2.ef \(\chi_{6624}(53, \cdot)\) n/a 15360 40
6624.2.ej \(\chi_{6624}(25, \cdot)\) None 0 40
6624.2.ek \(\chi_{6624}(7, \cdot)\) None 0 40
6624.2.en \(\chi_{6624}(281, \cdot)\) None 0 40
6624.2.eo \(\chi_{6624}(119, \cdot)\) None 0 40
6624.2.eq \(\chi_{6624}(43, \cdot)\) n/a 91840 80
6624.2.er \(\chi_{6624}(59, \cdot)\) n/a 91840 80
6624.2.ew \(\chi_{6624}(5, \cdot)\) n/a 91840 80
6624.2.ex \(\chi_{6624}(13, \cdot)\) n/a 91840 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6624))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6624)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(736))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(828))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1656))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6624))\)\(^{\oplus 1}\)