# Properties

 Label 8041.2 Level 8041 Weight 2 Dimension 2.58472e+06 Nonzero newspaces 80 Sturm bound 1.06445e+07

## Defining parameters

 Level: $$N$$ = $$8041 = 11 \cdot 17 \cdot 43$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$10644480$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8041))$$.

Total New Old
Modular forms 2674560 2606855 67705
Cusp forms 2647681 2584719 62962
Eisenstein series 26879 22136 4743

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8041))$$

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
8041.2.a $$\chi_{8041}(1, \cdot)$$ 8041.2.a.a 1 1
8041.2.a.b 1
8041.2.a.c 60
8041.2.a.d 62
8041.2.a.e 66
8041.2.a.f 66
8041.2.a.g 69
8041.2.a.h 74
8041.2.a.i 78
8041.2.a.j 82
8041.2.f $$\chi_{8041}(5677, \cdot)$$ n/a 628 1
8041.2.g $$\chi_{8041}(2364, \cdot)$$ n/a 704 1
8041.2.h $$\chi_{8041}(8040, \cdot)$$ n/a 788 1
8041.2.i $$\chi_{8041}(5424, \cdot)$$ n/a 1176 2
8041.2.j $$\chi_{8041}(472, \cdot)$$ n/a 1576 2
8041.2.k $$\chi_{8041}(6150, \cdot)$$ n/a 1256 2
8041.2.n $$\chi_{8041}(2194, \cdot)$$ n/a 2688 4
8041.2.s $$\chi_{8041}(2243, \cdot)$$ n/a 1576 2
8041.2.t $$\chi_{8041}(4608, \cdot)$$ n/a 1408 2
8041.2.u $$\chi_{8041}(3059, \cdot)$$ n/a 1320 2
8041.2.v $$\chi_{8041}(188, \cdot)$$ n/a 3504 6
8041.2.x $$\chi_{8041}(474, \cdot)$$ n/a 2528 4
8041.2.z $$\chi_{8041}(2837, \cdot)$$ n/a 3152 4
8041.2.ba $$\chi_{8041}(2923, \cdot)$$ n/a 3152 4
8041.2.bb $$\chi_{8041}(171, \cdot)$$ n/a 2816 4
8041.2.bc $$\chi_{8041}(1291, \cdot)$$ n/a 3024 4
8041.2.bh $$\chi_{8041}(3532, \cdot)$$ n/a 2640 4
8041.2.bi $$\chi_{8041}(2716, \cdot)$$ n/a 3152 4
8041.2.bl $$\chi_{8041}(2430, \cdot)$$ n/a 4728 6
8041.2.bm $$\chi_{8041}(441, \cdot)$$ n/a 3960 6
8041.2.bn $$\chi_{8041}(868, \cdot)$$ n/a 4224 6
8041.2.bs $$\chi_{8041}(1038, \cdot)$$ n/a 5632 8
8041.2.bt $$\chi_{8041}(1506, \cdot)$$ n/a 6048 8
8041.2.bu $$\chi_{8041}(386, \cdot)$$ n/a 5280 8
8041.2.bz $$\chi_{8041}(302, \cdot)$$ n/a 6048 8
8041.2.ca $$\chi_{8041}(3396, \cdot)$$ n/a 6304 8
8041.2.cb $$\chi_{8041}(375, \cdot)$$ n/a 7056 12
8041.2.cc $$\chi_{8041}(824, \cdot)$$ n/a 6304 8
8041.2.ce $$\chi_{8041}(1640, \cdot)$$ n/a 5280 8
8041.2.ci $$\chi_{8041}(914, \cdot)$$ n/a 7920 12
8041.2.cj $$\chi_{8041}(285, \cdot)$$ n/a 9456 12
8041.2.ck $$\chi_{8041}(135, \cdot)$$ n/a 6304 8
8041.2.cl $$\chi_{8041}(222, \cdot)$$ n/a 5632 8
8041.2.cm $$\chi_{8041}(50, \cdot)$$ n/a 6304 8
8041.2.cr $$\chi_{8041}(256, \cdot)$$ n/a 16896 24
8041.2.cs $$\chi_{8041}(128, \cdot)$$ n/a 12608 16
8041.2.cu $$\chi_{8041}(603, \cdot)$$ n/a 12096 16
8041.2.cw $$\chi_{8041}(120, \cdot)$$ n/a 8448 12
8041.2.cx $$\chi_{8041}(67, \cdot)$$ n/a 7920 12
8041.2.cy $$\chi_{8041}(373, \cdot)$$ n/a 9456 12
8041.2.df $$\chi_{8041}(1253, \cdot)$$ n/a 12608 16
8041.2.dg $$\chi_{8041}(265, \cdot)$$ n/a 10560 16
8041.2.dh $$\chi_{8041}(32, \cdot)$$ n/a 18912 24
8041.2.dj $$\chi_{8041}(342, \cdot)$$ n/a 15840 24
8041.2.dn $$\chi_{8041}(123, \cdot)$$ n/a 12608 16
8041.2.do $$\chi_{8041}(251, \cdot)$$ n/a 12608 16
8041.2.dt $$\chi_{8041}(409, \cdot)$$ n/a 16896 24
8041.2.du $$\chi_{8041}(16, \cdot)$$ n/a 18912 24
8041.2.dv $$\chi_{8041}(118, \cdot)$$ n/a 18912 24
8041.2.dy $$\chi_{8041}(214, \cdot)$$ n/a 25216 32
8041.2.dz $$\chi_{8041}(173, \cdot)$$ n/a 24192 32
8041.2.ec $$\chi_{8041}(98, \cdot)$$ n/a 18912 24
8041.2.ed $$\chi_{8041}(353, \cdot)$$ n/a 15840 24
8041.2.ee $$\chi_{8041}(103, \cdot)$$ n/a 33792 48
8041.2.eh $$\chi_{8041}(45, \cdot)$$ n/a 31680 48
8041.2.ei $$\chi_{8041}(54, \cdot)$$ n/a 37824 48
8041.2.ek $$\chi_{8041}(36, \cdot)$$ n/a 25216 32
8041.2.em $$\chi_{8041}(338, \cdot)$$ n/a 25216 32
8041.2.en $$\chi_{8041}(217, \cdot)$$ n/a 37824 48
8041.2.eo $$\chi_{8041}(4, \cdot)$$ n/a 37824 48
8041.2.es $$\chi_{8041}(100, \cdot)$$ n/a 31680 48
8041.2.eu $$\chi_{8041}(76, \cdot)$$ n/a 37824 48
8041.2.ez $$\chi_{8041}(288, \cdot)$$ n/a 37824 48
8041.2.fa $$\chi_{8041}(152, \cdot)$$ n/a 37824 48
8041.2.fb $$\chi_{8041}(18, \cdot)$$ n/a 33792 48
8041.2.fc $$\chi_{8041}(37, \cdot)$$ n/a 50432 64
8041.2.fd $$\chi_{8041}(6, \cdot)$$ n/a 50432 64
8041.2.fh $$\chi_{8041}(59, \cdot)$$ n/a 75648 96
8041.2.fj $$\chi_{8041}(2, \cdot)$$ n/a 75648 96
8041.2.fk $$\chi_{8041}(12, \cdot)$$ n/a 63360 96
8041.2.fl $$\chi_{8041}(10, \cdot)$$ n/a 75648 96
8041.2.fo $$\chi_{8041}(38, \cdot)$$ n/a 75648 96
8041.2.fp $$\chi_{8041}(30, \cdot)$$ n/a 75648 96
8041.2.fs $$\chi_{8041}(41, \cdot)$$ n/a 151296 192
8041.2.ft $$\chi_{8041}(27, \cdot)$$ n/a 151296 192
8041.2.fw $$\chi_{8041}(19, \cdot)$$ n/a 151296 192
8041.2.fy $$\chi_{8041}(9, \cdot)$$ n/a 151296 192
8041.2.gc $$\chi_{8041}(24, \cdot)$$ n/a 302592 384
8041.2.gd $$\chi_{8041}(3, \cdot)$$ n/a 302592 384

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8041))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8041)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(43))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(187))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(473))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(731))$$$$^{\oplus 2}$$