# Properties

 Label 8020.2 Level 8020 Weight 2 Dimension 1.02939e+06 Nonzero newspaces 54 Sturm bound 7.7184e+06

## Defining parameters

 Level: $$N$$ = $$8020 = 2^{2} \cdot 5 \cdot 401$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$54$$ Sturm bound: $$7718400$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8020))$$.

Total New Old
Modular forms 1937600 1034178 903422
Cusp forms 1921601 1029394 892207
Eisenstein series 15999 4784 11215

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8020))$$

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
8020.2.a $$\chi_{8020}(1, \cdot)$$ 8020.2.a.a 1 1
8020.2.a.b 2
8020.2.a.c 28
8020.2.a.d 29
8020.2.a.e 35
8020.2.a.f 37
8020.2.c $$\chi_{8020}(3209, \cdot)$$ n/a 200 1
8020.2.e $$\chi_{8020}(801, \cdot)$$ n/a 134 1
8020.2.g $$\chi_{8020}(4009, \cdot)$$ n/a 200 1
8020.2.j $$\chi_{8020}(1183, \cdot)$$ n/a 2404 2
8020.2.k $$\chi_{8020}(381, \cdot)$$ n/a 268 2
8020.2.m $$\chi_{8020}(1603, \cdot)$$ n/a 2404 2
8020.2.n $$\chi_{8020}(803, \cdot)$$ n/a 2400 2
8020.2.q $$\chi_{8020}(3589, \cdot)$$ n/a 400 2
8020.2.t $$\chi_{8020}(1223, \cdot)$$ n/a 2404 2
8020.2.u $$\chi_{8020}(841, \cdot)$$ n/a 536 4
8020.2.w $$\chi_{8020}(303, \cdot)$$ n/a 4808 4
8020.2.z $$\chi_{8020}(1301, \cdot)$$ n/a 536 4
8020.2.ba $$\chi_{8020}(1649, \cdot)$$ n/a 808 4
8020.2.bc $$\chi_{8020}(1907, \cdot)$$ n/a 4808 4
8020.2.be $$\chi_{8020}(29, \cdot)$$ n/a 800 4
8020.2.bg $$\chi_{8020}(4841, \cdot)$$ n/a 536 4
8020.2.bi $$\chi_{8020}(4049, \cdot)$$ n/a 800 4
8020.2.bk $$\chi_{8020}(371, \cdot)$$ n/a 6432 8
8020.2.bl $$\chi_{8020}(199, \cdot)$$ n/a 9616 8
8020.2.bo $$\chi_{8020}(1173, \cdot)$$ n/a 1608 8
8020.2.bp $$\chi_{8020}(133, \cdot)$$ n/a 1608 8
8020.2.bs $$\chi_{8020}(623, \cdot)$$ n/a 9616 8
8020.2.bv $$\chi_{8020}(1949, \cdot)$$ n/a 1600 8
8020.2.by $$\chi_{8020}(1643, \cdot)$$ n/a 9616 8
8020.2.bz $$\chi_{8020}(83, \cdot)$$ n/a 9616 8
8020.2.cb $$\chi_{8020}(981, \cdot)$$ n/a 1072 8
8020.2.cc $$\chi_{8020}(423, \cdot)$$ n/a 9616 8
8020.2.ce $$\chi_{8020}(321, \cdot)$$ n/a 2680 20
8020.2.cg $$\chi_{8020}(287, \cdot)$$ n/a 19232 16
8020.2.cj $$\chi_{8020}(369, \cdot)$$ n/a 3232 16
8020.2.ck $$\chi_{8020}(1041, \cdot)$$ n/a 2144 16
8020.2.cm $$\chi_{8020}(527, \cdot)$$ n/a 19232 16
8020.2.cn $$\chi_{8020}(629, \cdot)$$ n/a 4000 20
8020.2.cq $$\chi_{8020}(41, \cdot)$$ n/a 2680 20
8020.2.cr $$\chi_{8020}(489, \cdot)$$ n/a 4000 20
8020.2.cu $$\chi_{8020}(119, \cdot)$$ n/a 38464 32
8020.2.cv $$\chi_{8020}(171, \cdot)$$ n/a 25728 32
8020.2.cy $$\chi_{8020}(153, \cdot)$$ n/a 6432 32
8020.2.cz $$\chi_{8020}(33, \cdot)$$ n/a 6432 32
8020.2.dc $$\chi_{8020}(81, \cdot)$$ n/a 5360 40
8020.2.dd $$\chi_{8020}(49, \cdot)$$ n/a 8000 40
8020.2.dg $$\chi_{8020}(307, \cdot)$$ n/a 48080 40
8020.2.di $$\chi_{8020}(63, \cdot)$$ n/a 48080 40
8020.2.dj $$\chi_{8020}(223, \cdot)$$ n/a 48080 40
8020.2.dm $$\chi_{8020}(183, \cdot)$$ n/a 48080 40
8020.2.do $$\chi_{8020}(181, \cdot)$$ n/a 10720 80
8020.2.dp $$\chi_{8020}(9, \cdot)$$ n/a 16160 80
8020.2.ds $$\chi_{8020}(7, \cdot)$$ n/a 96160 80
8020.2.dt $$\chi_{8020}(43, \cdot)$$ n/a 96160 80
8020.2.dy $$\chi_{8020}(17, \cdot)$$ n/a 32160 160
8020.2.dz $$\chi_{8020}(13, \cdot)$$ n/a 32160 160
8020.2.ec $$\chi_{8020}(31, \cdot)$$ n/a 128640 160
8020.2.ed $$\chi_{8020}(19, \cdot)$$ n/a 192320 160

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8020))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8020)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(401))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(802))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1604))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2005))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4010))$$$$^{\oplus 2}$$