Properties

Label 8041.2
Level 8041
Weight 2
Dimension 2584719
Nonzero newspaces 80
Sturm bound 10644480

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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

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