Properties

Label 8021.2
Level 8021
Weight 2
Dimension 2626311
Nonzero newspaces 64
Sturm bound 10659264

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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

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