# Properties

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

## 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

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