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Properties

Label 6288.2
Level 6288
Weight 2
Dimension 462104
Nonzero newspaces 32
Sturm bound 4392960

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Defining parameters

Level: \( N \) = \( 6288 = 2^{4} \cdot 3 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(4392960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6288))\).

Total New Old
Modular forms 1105520 464428 641092
Cusp forms 1090961 462104 628857
Eisenstein series 14559 2324 12235

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6288))\)

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
6288.2.a \(\chi_{6288}(1, \cdot)\) 6288.2.a.a 1 1
6288.2.a.b 1
6288.2.a.c 1
6288.2.a.d 1
6288.2.a.e 1
6288.2.a.f 1
6288.2.a.g 1
6288.2.a.h 1
6288.2.a.i 1
6288.2.a.j 1
6288.2.a.k 1
6288.2.a.l 1
6288.2.a.m 1
6288.2.a.n 1
6288.2.a.o 1
6288.2.a.p 1
6288.2.a.q 1
6288.2.a.r 1
6288.2.a.s 2
6288.2.a.t 2
6288.2.a.u 2
6288.2.a.v 3
6288.2.a.w 3
6288.2.a.x 3
6288.2.a.y 4
6288.2.a.z 4
6288.2.a.ba 4
6288.2.a.bb 4
6288.2.a.bc 4
6288.2.a.bd 5
6288.2.a.be 5
6288.2.a.bf 5
6288.2.a.bg 5
6288.2.a.bh 6
6288.2.a.bi 6
6288.2.a.bj 6
6288.2.a.bk 6
6288.2.a.bl 6
6288.2.a.bm 8
6288.2.a.bn 8
6288.2.a.bo 11
6288.2.b \(\chi_{6288}(5239, \cdot)\) None 0 1
6288.2.d \(\chi_{6288}(3407, \cdot)\) n/a 260 1
6288.2.g \(\chi_{6288}(3145, \cdot)\) None 0 1
6288.2.i \(\chi_{6288}(785, \cdot)\) n/a 262 1
6288.2.j \(\chi_{6288}(263, \cdot)\) None 0 1
6288.2.l \(\chi_{6288}(2095, \cdot)\) n/a 132 1
6288.2.o \(\chi_{6288}(3929, \cdot)\) None 0 1
6288.2.s \(\chi_{6288}(2357, \cdot)\) n/a 2104 2
6288.2.t \(\chi_{6288}(1573, \cdot)\) n/a 1040 2
6288.2.u \(\chi_{6288}(1835, \cdot)\) n/a 2080 2
6288.2.v \(\chi_{6288}(523, \cdot)\) n/a 1056 2
6288.2.y \(\chi_{6288}(577, \cdot)\) n/a 528 4
6288.2.ba \(\chi_{6288}(2297, \cdot)\) None 0 4
6288.2.bd \(\chi_{6288}(463, \cdot)\) n/a 528 4
6288.2.bf \(\chi_{6288}(839, \cdot)\) None 0 4
6288.2.bg \(\chi_{6288}(209, \cdot)\) n/a 1048 4
6288.2.bi \(\chi_{6288}(2185, \cdot)\) None 0 4
6288.2.bl \(\chi_{6288}(2447, \cdot)\) n/a 1056 4
6288.2.bn \(\chi_{6288}(3607, \cdot)\) None 0 4
6288.2.bo \(\chi_{6288}(193, \cdot)\) n/a 1584 12
6288.2.br \(\chi_{6288}(859, \cdot)\) n/a 4224 8
6288.2.bs \(\chi_{6288}(323, \cdot)\) n/a 8416 8
6288.2.bt \(\chi_{6288}(61, \cdot)\) n/a 4224 8
6288.2.bu \(\chi_{6288}(173, \cdot)\) n/a 8416 8
6288.2.by \(\chi_{6288}(281, \cdot)\) None 0 12
6288.2.cb \(\chi_{6288}(79, \cdot)\) n/a 1584 12
6288.2.cd \(\chi_{6288}(215, \cdot)\) None 0 12
6288.2.ce \(\chi_{6288}(593, \cdot)\) n/a 3144 12
6288.2.cg \(\chi_{6288}(361, \cdot)\) None 0 12
6288.2.cj \(\chi_{6288}(191, \cdot)\) n/a 3168 12
6288.2.cl \(\chi_{6288}(199, \cdot)\) None 0 12
6288.2.co \(\chi_{6288}(19, \cdot)\) n/a 12672 24
6288.2.cp \(\chi_{6288}(107, \cdot)\) n/a 25248 24
6288.2.cq \(\chi_{6288}(301, \cdot)\) n/a 12672 24
6288.2.cr \(\chi_{6288}(149, \cdot)\) n/a 25248 24
6288.2.cu \(\chi_{6288}(49, \cdot)\) n/a 6336 48
6288.2.cv \(\chi_{6288}(103, \cdot)\) None 0 48
6288.2.cx \(\chi_{6288}(143, \cdot)\) n/a 12672 48
6288.2.da \(\chi_{6288}(25, \cdot)\) None 0 48
6288.2.dc \(\chi_{6288}(17, \cdot)\) n/a 12576 48
6288.2.dd \(\chi_{6288}(167, \cdot)\) None 0 48
6288.2.df \(\chi_{6288}(31, \cdot)\) n/a 6336 48
6288.2.di \(\chi_{6288}(137, \cdot)\) None 0 48
6288.2.dm \(\chi_{6288}(29, \cdot)\) n/a 100992 96
6288.2.dn \(\chi_{6288}(13, \cdot)\) n/a 50688 96
6288.2.do \(\chi_{6288}(11, \cdot)\) n/a 100992 96
6288.2.dp \(\chi_{6288}(67, \cdot)\) n/a 50688 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6288))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6288)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(131))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(262))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(393))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(524))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(786))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1048))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1572))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2096))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3144))\)\(^{\oplus 2}\)