Properties

Label 8020.2
Level 8020
Weight 2
Dimension 1029394
Nonzero newspaces 54
Sturm bound 7718400

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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

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