Properties

Label 6004.2
Level 6004
Weight 2
Dimension 648734
Nonzero newspaces 64
Sturm bound 4492800

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Defining parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(4492800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6004))\).

Total New Old
Modular forms 1130220 653966 476254
Cusp forms 1116181 648734 467447
Eisenstein series 14039 5232 8807

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6004))\)

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
6004.2.a \(\chi_{6004}(1, \cdot)\) 6004.2.a.a 1 1
6004.2.a.b 1
6004.2.a.c 1
6004.2.a.d 8
6004.2.a.e 24
6004.2.a.f 25
6004.2.a.g 27
6004.2.a.h 31
6004.2.f \(\chi_{6004}(3951, \cdot)\) n/a 780 1
6004.2.g \(\chi_{6004}(3001, \cdot)\) n/a 132 1
6004.2.h \(\chi_{6004}(5055, \cdot)\) n/a 720 1
6004.2.i \(\chi_{6004}(1445, \cdot)\) n/a 240 2
6004.2.j \(\chi_{6004}(1265, \cdot)\) n/a 260 2
6004.2.k \(\chi_{6004}(4605, \cdot)\) n/a 268 2
6004.2.l \(\chi_{6004}(1793, \cdot)\) n/a 268 2
6004.2.q \(\chi_{6004}(791, \cdot)\) n/a 1560 2
6004.2.r \(\chi_{6004}(1737, \cdot)\) n/a 264 2
6004.2.s \(\chi_{6004}(419, \cdot)\) n/a 1440 2
6004.2.t \(\chi_{6004}(1557, \cdot)\) n/a 268 2
6004.2.u \(\chi_{6004}(2583, \cdot)\) n/a 1592 2
6004.2.v \(\chi_{6004}(315, \cdot)\) n/a 1592 2
6004.2.w \(\chi_{6004}(767, \cdot)\) n/a 1592 2
6004.2.x \(\chi_{6004}(3105, \cdot)\) n/a 268 2
6004.2.y \(\chi_{6004}(1319, \cdot)\) n/a 1592 2
6004.2.bl \(\chi_{6004}(3579, \cdot)\) n/a 1592 2
6004.2.bm \(\chi_{6004}(293, \cdot)\) n/a 268 2
6004.2.bn \(\chi_{6004}(4131, \cdot)\) n/a 1592 2
6004.2.bo \(\chi_{6004}(633, \cdot)\) n/a 780 6
6004.2.bp \(\chi_{6004}(529, \cdot)\) n/a 798 6
6004.2.bq \(\chi_{6004}(213, \cdot)\) n/a 798 6
6004.2.br \(\chi_{6004}(381, \cdot)\) n/a 1440 12
6004.2.bs \(\chi_{6004}(2157, \cdot)\) n/a 798 6
6004.2.bu \(\chi_{6004}(371, \cdot)\) n/a 4776 6
6004.2.bw \(\chi_{6004}(2315, \cdot)\) n/a 4776 6
6004.2.bz \(\chi_{6004}(631, \cdot)\) n/a 4776 6
6004.2.cc \(\chi_{6004}(687, \cdot)\) n/a 4776 6
6004.2.ce \(\chi_{6004}(789, \cdot)\) n/a 804 6
6004.2.cg \(\chi_{6004}(1739, \cdot)\) n/a 4680 6
6004.2.ci \(\chi_{6004}(261, \cdot)\) n/a 798 6
6004.2.cl \(\chi_{6004}(1051, \cdot)\) n/a 4776 6
6004.2.cn \(\chi_{6004}(191, \cdot)\) n/a 8640 12
6004.2.co \(\chi_{6004}(1177, \cdot)\) n/a 1584 12
6004.2.cp \(\chi_{6004}(1443, \cdot)\) n/a 9552 12
6004.2.cu \(\chi_{6004}(45, \cdot)\) n/a 3216 24
6004.2.cv \(\chi_{6004}(49, \cdot)\) n/a 3216 24
6004.2.cw \(\chi_{6004}(125, \cdot)\) n/a 3168 24
6004.2.cx \(\chi_{6004}(761, \cdot)\) n/a 2880 24
6004.2.cy \(\chi_{6004}(183, \cdot)\) n/a 19104 24
6004.2.cz \(\chi_{6004}(145, \cdot)\) n/a 3216 24
6004.2.da \(\chi_{6004}(235, \cdot)\) n/a 19104 24
6004.2.dn \(\chi_{6004}(31, \cdot)\) n/a 19104 24
6004.2.do \(\chi_{6004}(217, \cdot)\) n/a 3216 24
6004.2.dp \(\chi_{6004}(7, \cdot)\) n/a 19104 24
6004.2.dq \(\chi_{6004}(387, \cdot)\) n/a 19104 24
6004.2.dr \(\chi_{6004}(151, \cdot)\) n/a 19104 24
6004.2.ds \(\chi_{6004}(37, \cdot)\) n/a 3216 24
6004.2.dt \(\chi_{6004}(39, \cdot)\) n/a 17280 24
6004.2.du \(\chi_{6004}(69, \cdot)\) n/a 3168 24
6004.2.dv \(\chi_{6004}(179, \cdot)\) n/a 19104 24
6004.2.ea \(\chi_{6004}(5, \cdot)\) n/a 9576 72
6004.2.eb \(\chi_{6004}(9, \cdot)\) n/a 9576 72
6004.2.ec \(\chi_{6004}(101, \cdot)\) n/a 9648 72
6004.2.ee \(\chi_{6004}(63, \cdot)\) n/a 57312 72
6004.2.eh \(\chi_{6004}(29, \cdot)\) n/a 9576 72
6004.2.ej \(\chi_{6004}(67, \cdot)\) n/a 57312 72
6004.2.el \(\chi_{6004}(33, \cdot)\) n/a 9648 72
6004.2.en \(\chi_{6004}(155, \cdot)\) n/a 57312 72
6004.2.eq \(\chi_{6004}(175, \cdot)\) n/a 57312 72
6004.2.et \(\chi_{6004}(35, \cdot)\) n/a 57312 72
6004.2.ev \(\chi_{6004}(51, \cdot)\) n/a 57312 72
6004.2.ex \(\chi_{6004}(345, \cdot)\) n/a 9576 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(158))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(316))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1501))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3002))\)\(^{\oplus 2}\)