Properties

Label 8281.2
Level 8281
Weight 2
Dimension 2628608
Nonzero newspaces 60
Sturm bound 11129664

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Defining parameters

Level: \( N \) = \( 8281 = 7^{2} \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(11129664\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8281))\).

Total New Old
Modular forms 2796096 2648445 147651
Cusp forms 2768737 2628608 140129
Eisenstein series 27359 19837 7522

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8281))\)

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
8281.2.a \(\chi_{8281}(1, \cdot)\) 8281.2.a.a 1 1
8281.2.a.b 1
8281.2.a.c 1
8281.2.a.d 1
8281.2.a.e 1
8281.2.a.f 1
8281.2.a.g 1
8281.2.a.h 1
8281.2.a.i 1
8281.2.a.j 1
8281.2.a.k 1
8281.2.a.l 1
8281.2.a.m 1
8281.2.a.n 2
8281.2.a.o 2
8281.2.a.p 2
8281.2.a.q 2
8281.2.a.r 2
8281.2.a.s 2
8281.2.a.t 2
8281.2.a.u 2
8281.2.a.v 2
8281.2.a.w 2
8281.2.a.x 2
8281.2.a.y 2
8281.2.a.z 2
8281.2.a.ba 2
8281.2.a.bb 2
8281.2.a.bc 3
8281.2.a.bd 3
8281.2.a.be 3
8281.2.a.bf 3
8281.2.a.bg 3
8281.2.a.bh 3
8281.2.a.bi 3
8281.2.a.bj 3
8281.2.a.bk 3
8281.2.a.bl 3
8281.2.a.bm 3
8281.2.a.bn 4
8281.2.a.bo 4
8281.2.a.bp 4
8281.2.a.bq 4
8281.2.a.br 4
8281.2.a.bs 4
8281.2.a.bt 4
8281.2.a.bu 4
8281.2.a.bv 4
8281.2.a.bw 5
8281.2.a.bx 5
8281.2.a.by 6
8281.2.a.bz 6
8281.2.a.ca 6
8281.2.a.cb 6
8281.2.a.cc 6
8281.2.a.cd 6
8281.2.a.ce 6
8281.2.a.cf 6
8281.2.a.cg 6
8281.2.a.ch 6
8281.2.a.ci 8
8281.2.a.cj 8
8281.2.a.ck 8
8281.2.a.cl 8
8281.2.a.cm 12
8281.2.a.cn 12
8281.2.a.co 12
8281.2.a.cp 12
8281.2.a.cq 12
8281.2.a.cr 12
8281.2.a.cs 16
8281.2.a.ct 24
8281.2.a.cu 24
8281.2.a.cv 24
8281.2.a.cw 24
8281.2.a.cx 32
8281.2.a.cy 36
8281.2.a.cz 36
8281.2.c \(\chi_{8281}(1520, \cdot)\) n/a 500 1
8281.2.e \(\chi_{8281}(508, \cdot)\) n/a 990 2
8281.2.f \(\chi_{8281}(1667, \cdot)\) n/a 1004 2
8281.2.g \(\chi_{8281}(2174, \cdot)\) n/a 986 2
8281.2.h \(\chi_{8281}(3019, \cdot)\) n/a 986 2
8281.2.i \(\chi_{8281}(6859, \cdot)\) n/a 984 2
8281.2.k \(\chi_{8281}(1206, \cdot)\) n/a 986 2
8281.2.q \(\chi_{8281}(5048, \cdot)\) n/a 1002 2
8281.2.r \(\chi_{8281}(2027, \cdot)\) n/a 988 2
8281.2.u \(\chi_{8281}(361, \cdot)\) n/a 986 2
8281.2.w \(\chi_{8281}(1184, \cdot)\) n/a 4278 6
8281.2.x \(\chi_{8281}(19, \cdot)\) n/a 1972 4
8281.2.bb \(\chi_{8281}(864, \cdot)\) n/a 1972 4
8281.2.bc \(\chi_{8281}(5507, \cdot)\) n/a 1976 4
8281.2.bd \(\chi_{8281}(587, \cdot)\) n/a 1976 4
8281.2.bf \(\chi_{8281}(638, \cdot)\) n/a 7404 12
8281.2.bh \(\chi_{8281}(337, \cdot)\) n/a 4260 6
8281.2.bj \(\chi_{8281}(529, \cdot)\) n/a 8508 12
8281.2.bk \(\chi_{8281}(191, \cdot)\) n/a 8508 12
8281.2.bl \(\chi_{8281}(22, \cdot)\) n/a 8496 12
8281.2.bm \(\chi_{8281}(170, \cdot)\) n/a 8544 12
8281.2.bo \(\chi_{8281}(246, \cdot)\) n/a 7416 12
8281.2.br \(\chi_{8281}(944, \cdot)\) n/a 8520 12
8281.2.bs \(\chi_{8281}(165, \cdot)\) n/a 14472 24
8281.2.bt \(\chi_{8281}(263, \cdot)\) n/a 14472 24
8281.2.bu \(\chi_{8281}(295, \cdot)\) n/a 14784 24
8281.2.bv \(\chi_{8281}(79, \cdot)\) n/a 14448 24
8281.2.bx \(\chi_{8281}(485, \cdot)\) n/a 8508 12
8281.2.ca \(\chi_{8281}(506, \cdot)\) n/a 8496 12
8281.2.cb \(\chi_{8281}(316, \cdot)\) n/a 8496 12
8281.2.ch \(\chi_{8281}(23, \cdot)\) n/a 8508 12
8281.2.cj \(\chi_{8281}(489, \cdot)\) n/a 14496 24
8281.2.cl \(\chi_{8281}(30, \cdot)\) n/a 14472 24
8281.2.co \(\chi_{8281}(116, \cdot)\) n/a 14448 24
8281.2.cp \(\chi_{8281}(491, \cdot)\) n/a 14808 24
8281.2.cv \(\chi_{8281}(459, \cdot)\) n/a 14472 24
8281.2.cx \(\chi_{8281}(188, \cdot)\) n/a 16992 24
8281.2.cy \(\chi_{8281}(437, \cdot)\) n/a 16992 24
8281.2.cz \(\chi_{8281}(89, \cdot)\) n/a 17016 24
8281.2.dd \(\chi_{8281}(488, \cdot)\) n/a 17016 24
8281.2.de \(\chi_{8281}(92, \cdot)\) n/a 60912 72
8281.2.dg \(\chi_{8281}(97, \cdot)\) n/a 28896 48
8281.2.dh \(\chi_{8281}(31, \cdot)\) n/a 28896 48
8281.2.di \(\chi_{8281}(227, \cdot)\) n/a 28944 48
8281.2.dm \(\chi_{8281}(215, \cdot)\) n/a 28944 48
8281.2.do \(\chi_{8281}(64, \cdot)\) n/a 60912 72
8281.2.dq \(\chi_{8281}(53, \cdot)\) n/a 122112 144
8281.2.dr \(\chi_{8281}(29, \cdot)\) n/a 122112 144
8281.2.ds \(\chi_{8281}(9, \cdot)\) n/a 121968 144
8281.2.dt \(\chi_{8281}(16, \cdot)\) n/a 121968 144
8281.2.du \(\chi_{8281}(34, \cdot)\) n/a 121824 144
8281.2.dw \(\chi_{8281}(4, \cdot)\) n/a 121968 144
8281.2.ec \(\chi_{8281}(36, \cdot)\) n/a 122112 144
8281.2.ed \(\chi_{8281}(25, \cdot)\) n/a 122112 144
8281.2.eg \(\chi_{8281}(88, \cdot)\) n/a 121968 144
8281.2.ei \(\chi_{8281}(24, \cdot)\) n/a 243936 288
8281.2.em \(\chi_{8281}(45, \cdot)\) n/a 243936 288
8281.2.en \(\chi_{8281}(5, \cdot)\) n/a 244224 288
8281.2.eo \(\chi_{8281}(6, \cdot)\) n/a 244224 288

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8281))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8281)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(637))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 2}\)