Properties

Label 8004.2
Level 8004
Weight 2
Dimension 769108
Nonzero newspaces 48
Sturm bound 7096320

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Defining parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(7096320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8004))\).

Total New Old
Modular forms 1786400 773652 1012748
Cusp forms 1761761 769108 992653
Eisenstein series 24639 4544 20095

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8004))\)

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
8004.2.a \(\chi_{8004}(1, \cdot)\) 8004.2.a.a 1 1
8004.2.a.b 1
8004.2.a.c 1
8004.2.a.d 8
8004.2.a.e 9
8004.2.a.f 9
8004.2.a.g 12
8004.2.a.h 13
8004.2.a.i 16
8004.2.a.j 16
8004.2.a.k 18
8004.2.c \(\chi_{8004}(5567, \cdot)\) n/a 1320 1
8004.2.d \(\chi_{8004}(6671, \cdot)\) n/a 1232 1
8004.2.g \(\chi_{8004}(5335, \cdot)\) n/a 720 1
8004.2.h \(\chi_{8004}(6439, \cdot)\) n/a 672 1
8004.2.j \(\chi_{8004}(4001, \cdot)\) n/a 240 1
8004.2.m \(\chi_{8004}(5105, \cdot)\) n/a 224 1
8004.2.n \(\chi_{8004}(6901, \cdot)\) n/a 108 1
8004.2.q \(\chi_{8004}(2071, \cdot)\) n/a 1320 2
8004.2.s \(\chi_{8004}(1931, \cdot)\) n/a 2864 2
8004.2.u \(\chi_{8004}(505, \cdot)\) n/a 240 2
8004.2.w \(\chi_{8004}(737, \cdot)\) n/a 440 2
8004.2.y \(\chi_{8004}(277, \cdot)\) n/a 672 6
8004.2.z \(\chi_{8004}(349, \cdot)\) n/a 1120 10
8004.2.bb \(\chi_{8004}(1657, \cdot)\) n/a 648 6
8004.2.be \(\chi_{8004}(413, \cdot)\) n/a 1440 6
8004.2.bf \(\chi_{8004}(689, \cdot)\) n/a 1440 6
8004.2.bh \(\chi_{8004}(919, \cdot)\) n/a 4320 6
8004.2.bk \(\chi_{8004}(91, \cdot)\) n/a 4320 6
8004.2.bl \(\chi_{8004}(1151, \cdot)\) n/a 7920 6
8004.2.bo \(\chi_{8004}(323, \cdot)\) n/a 7920 6
8004.2.br \(\chi_{8004}(289, \cdot)\) n/a 1200 10
8004.2.bs \(\chi_{8004}(1625, \cdot)\) n/a 2240 10
8004.2.bv \(\chi_{8004}(521, \cdot)\) n/a 2400 10
8004.2.bx \(\chi_{8004}(175, \cdot)\) n/a 6720 10
8004.2.by \(\chi_{8004}(1855, \cdot)\) n/a 7200 10
8004.2.cb \(\chi_{8004}(59, \cdot)\) n/a 13440 10
8004.2.cc \(\chi_{8004}(347, \cdot)\) n/a 14320 10
8004.2.cf \(\chi_{8004}(185, \cdot)\) n/a 2640 12
8004.2.ch \(\chi_{8004}(229, \cdot)\) n/a 1440 12
8004.2.cj \(\chi_{8004}(275, \cdot)\) n/a 17184 12
8004.2.cl \(\chi_{8004}(967, \cdot)\) n/a 7920 12
8004.2.cn \(\chi_{8004}(41, \cdot)\) n/a 4800 20
8004.2.cp \(\chi_{8004}(157, \cdot)\) n/a 2400 20
8004.2.cr \(\chi_{8004}(191, \cdot)\) n/a 28640 20
8004.2.ct \(\chi_{8004}(307, \cdot)\) n/a 14400 20
8004.2.cu \(\chi_{8004}(25, \cdot)\) n/a 7200 60
8004.2.cv \(\chi_{8004}(35, \cdot)\) n/a 85920 60
8004.2.cy \(\chi_{8004}(239, \cdot)\) n/a 85920 60
8004.2.cz \(\chi_{8004}(67, \cdot)\) n/a 43200 60
8004.2.dc \(\chi_{8004}(7, \cdot)\) n/a 43200 60
8004.2.de \(\chi_{8004}(5, \cdot)\) n/a 14400 60
8004.2.df \(\chi_{8004}(53, \cdot)\) n/a 14400 60
8004.2.di \(\chi_{8004}(13, \cdot)\) n/a 7200 60
8004.2.dk \(\chi_{8004}(31, \cdot)\) n/a 86400 120
8004.2.dm \(\chi_{8004}(11, \cdot)\) n/a 171840 120
8004.2.do \(\chi_{8004}(37, \cdot)\) n/a 14400 120
8004.2.dq \(\chi_{8004}(77, \cdot)\) n/a 28800 120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(667))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2001))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2668))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4002))\)\(^{\oplus 2}\)