# Properties

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

## 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 available 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

$$S_{2}^{\mathrm{old}}(\Gamma_1(8281)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(637))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1183))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8281))$$$$^{\oplus 1}$$