# Properties

 Label 8021.2 Level 8021 Weight 2 Dimension 2.62631e+06 Nonzero newspaces 64 Sturm bound 1.06593e+07

## Defining parameters

 Level: $$N$$ = $$8021 = 13 \cdot 617$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$64$$ Sturm bound: $$10659264$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8021))$$.

Total New Old
Modular forms 2672208 2639843 32365
Cusp forms 2657425 2626311 31114
Eisenstein series 14783 13532 1251

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8021))$$

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
8021.2.a $$\chi_{8021}(1, \cdot)$$ 8021.2.a.a 134 1
8021.2.a.b 140
8021.2.a.c 169
8021.2.a.d 174
8021.2.b $$\chi_{8021}(8020, \cdot)$$ n/a 720 1
8021.2.c $$\chi_{8021}(2469, \cdot)$$ n/a 720 1
8021.2.d $$\chi_{8021}(5552, \cdot)$$ n/a 618 1
8021.2.e $$\chi_{8021}(5554, \cdot)$$ n/a 1436 2
8021.2.f $$\chi_{8021}(194, \cdot)$$ n/a 1436 2
8021.2.k $$\chi_{8021}(5747, \cdot)$$ n/a 1236 2
8021.2.l $$\chi_{8021}(3084, \cdot)$$ n/a 1436 2
8021.2.m $$\chi_{8021}(4320, \cdot)$$ n/a 1436 2
8021.2.n $$\chi_{8021}(1850, \cdot)$$ n/a 1440 2
8021.2.o $$\chi_{8021}(2302, \cdot)$$ n/a 3708 6
8021.2.q $$\chi_{8021}(1373, \cdot)$$ n/a 2876 4
8021.2.r $$\chi_{8021}(5075, \cdot)$$ n/a 2876 4
8021.2.t $$\chi_{8021}(1106, \cdot)$$ n/a 6180 10
8021.2.u $$\chi_{8021}(3279, \cdot)$$ n/a 2880 4
8021.2.z $$\chi_{8021}(2045, \cdot)$$ n/a 2872 4
8021.2.ba $$\chi_{8021}(209, \cdot)$$ n/a 3708 6
8021.2.bb $$\chi_{8021}(142, \cdot)$$ n/a 4320 6
8021.2.bc $$\chi_{8021}(2326, \cdot)$$ n/a 4320 6
8021.2.bd $$\chi_{8021}(451, \cdot)$$ n/a 8616 12
8021.2.be $$\chi_{8021}(586, \cdot)$$ n/a 6180 10
8021.2.bf $$\chi_{8021}(792, \cdot)$$ n/a 7200 10
8021.2.bg $$\chi_{8021}(805, \cdot)$$ n/a 7200 10
8021.2.bi $$\chi_{8021}(756, \cdot)$$ n/a 5752 8
8021.2.bj $$\chi_{8021}(435, \cdot)$$ n/a 5752 8
8021.2.bl $$\chi_{8021}(1470, \cdot)$$ n/a 7416 12
8021.2.bq $$\chi_{8021}(441, \cdot)$$ n/a 8616 12
8021.2.br $$\chi_{8021}(113, \cdot)$$ n/a 14360 20
8021.2.bs $$\chi_{8021}(62, \cdot)$$ n/a 8640 12
8021.2.bt $$\chi_{8021}(420, \cdot)$$ n/a 8640 12
8021.2.bu $$\chi_{8021}(126, \cdot)$$ n/a 8616 12
8021.2.bv $$\chi_{8021}(157, \cdot)$$ n/a 12360 20
8021.2.ca $$\chi_{8021}(1078, \cdot)$$ n/a 14360 20
8021.2.cc $$\chi_{8021}(21, \cdot)$$ n/a 17256 24
8021.2.cd $$\chi_{8021}(70, \cdot)$$ n/a 17256 24
8021.2.cf $$\chi_{8021}(199, \cdot)$$ n/a 14400 20
8021.2.cg $$\chi_{8021}(342, \cdot)$$ n/a 14400 20
8021.2.ch $$\chi_{8021}(1121, \cdot)$$ n/a 14360 20
8021.2.ci $$\chi_{8021}(105, \cdot)$$ n/a 37080 60
8021.2.cj $$\chi_{8021}(36, \cdot)$$ n/a 17232 24
8021.2.co $$\chi_{8021}(120, \cdot)$$ n/a 17280 24
8021.2.cq $$\chi_{8021}(73, \cdot)$$ n/a 28760 40
8021.2.cr $$\chi_{8021}(291, \cdot)$$ n/a 28760 40
8021.2.ct $$\chi_{8021}(69, \cdot)$$ n/a 28720 40
8021.2.cy $$\chi_{8021}(100, \cdot)$$ n/a 28800 40
8021.2.cz $$\chi_{8021}(51, \cdot)$$ n/a 43200 60
8021.2.da $$\chi_{8021}(64, \cdot)$$ n/a 43200 60
8021.2.db $$\chi_{8021}(196, \cdot)$$ n/a 37080 60
8021.2.dd $$\chi_{8021}(20, \cdot)$$ n/a 34512 48
8021.2.de $$\chi_{8021}(6, \cdot)$$ n/a 34512 48
8021.2.dg $$\chi_{8021}(16, \cdot)$$ n/a 86160 120
8021.2.di $$\chi_{8021}(46, \cdot)$$ n/a 57520 80
8021.2.dj $$\chi_{8021}(89, \cdot)$$ n/a 57520 80
8021.2.dl $$\chi_{8021}(25, \cdot)$$ n/a 86160 120
8021.2.dq $$\chi_{8021}(14, \cdot)$$ n/a 74160 120
8021.2.dr $$\chi_{8021}(81, \cdot)$$ n/a 86160 120
8021.2.ds $$\chi_{8021}(4, \cdot)$$ n/a 86400 120
8021.2.dt $$\chi_{8021}(43, \cdot)$$ n/a 86400 120
8021.2.dv $$\chi_{8021}(57, \cdot)$$ n/a 172560 240
8021.2.dw $$\chi_{8021}(5, \cdot)$$ n/a 172560 240
8021.2.dy $$\chi_{8021}(9, \cdot)$$ n/a 172800 240
8021.2.ed $$\chi_{8021}(30, \cdot)$$ n/a 172320 240
8021.2.ef $$\chi_{8021}(33, \cdot)$$ n/a 345120 480
8021.2.eg $$\chi_{8021}(24, \cdot)$$ n/a 345120 480

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8021))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8021)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(617))$$$$^{\oplus 2}$$