## 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

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