# Properties

 Label 7098.2 Level 7098 Weight 2 Dimension 322658 Nonzero newspaces 60 Sturm bound 5451264

## Defining parameters

 Level: $$N$$ = $$7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$5451264$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7098))$$.

Total New Old
Modular forms 1373760 322658 1051102
Cusp forms 1351873 322658 1029215
Eisenstein series 21887 0 21887

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7098))$$

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
7098.2.a $$\chi_{7098}(1, \cdot)$$ 7098.2.a.a 1 1
7098.2.a.b 1
7098.2.a.c 1
7098.2.a.d 1
7098.2.a.e 1
7098.2.a.f 1
7098.2.a.g 1
7098.2.a.h 1
7098.2.a.i 1
7098.2.a.j 1
7098.2.a.k 1
7098.2.a.l 1
7098.2.a.m 1
7098.2.a.n 1
7098.2.a.o 1
7098.2.a.p 1
7098.2.a.q 1
7098.2.a.r 1
7098.2.a.s 1
7098.2.a.t 1
7098.2.a.u 1
7098.2.a.v 1
7098.2.a.w 1
7098.2.a.x 1
7098.2.a.y 1
7098.2.a.z 1
7098.2.a.ba 1
7098.2.a.bb 1
7098.2.a.bc 1
7098.2.a.bd 1
7098.2.a.be 1
7098.2.a.bf 1
7098.2.a.bg 2
7098.2.a.bh 2
7098.2.a.bi 2
7098.2.a.bj 2
7098.2.a.bk 2
7098.2.a.bl 2
7098.2.a.bm 2
7098.2.a.bn 2
7098.2.a.bo 2
7098.2.a.bp 2
7098.2.a.bq 2
7098.2.a.br 2
7098.2.a.bs 2
7098.2.a.bt 2
7098.2.a.bu 2
7098.2.a.bv 2
7098.2.a.bw 2
7098.2.a.bx 2
7098.2.a.by 2
7098.2.a.bz 2
7098.2.a.ca 2
7098.2.a.cb 3
7098.2.a.cc 3
7098.2.a.cd 3
7098.2.a.ce 3
7098.2.a.cf 3
7098.2.a.cg 3
7098.2.a.ch 3
7098.2.a.ci 3
7098.2.a.cj 3
7098.2.a.ck 3
7098.2.a.cl 3
7098.2.a.cm 3
7098.2.a.cn 4
7098.2.a.co 4
7098.2.a.cp 6
7098.2.a.cq 6
7098.2.a.cr 6
7098.2.a.cs 6
7098.2.a.ct 6
7098.2.a.cu 6
7098.2.c $$\chi_{7098}(337, \cdot)$$ n/a 156 1
7098.2.e $$\chi_{7098}(7097, \cdot)$$ n/a 408 1
7098.2.g $$\chi_{7098}(6761, \cdot)$$ n/a 412 1
7098.2.i $$\chi_{7098}(4057, \cdot)$$ n/a 412 2
7098.2.j $$\chi_{7098}(529, \cdot)$$ n/a 412 2
7098.2.k $$\chi_{7098}(991, \cdot)$$ n/a 412 2
7098.2.l $$\chi_{7098}(3571, \cdot)$$ n/a 304 2
7098.2.o $$\chi_{7098}(4633, \cdot)$$ n/a 416 2
7098.2.p $$\chi_{7098}(239, \cdot)$$ n/a 616 2
7098.2.q $$\chi_{7098}(3065, \cdot)$$ n/a 824 2
7098.2.s $$\chi_{7098}(3403, \cdot)$$ n/a 312 2
7098.2.u $$\chi_{7098}(4247, \cdot)$$ n/a 820 2
7098.2.z $$\chi_{7098}(677, \cdot)$$ n/a 828 2
7098.2.bb $$\chi_{7098}(4709, \cdot)$$ n/a 820 2
7098.2.bd $$\chi_{7098}(361, \cdot)$$ n/a 412 2
7098.2.bg $$\chi_{7098}(1013, \cdot)$$ n/a 824 2
7098.2.bi $$\chi_{7098}(4079, \cdot)$$ n/a 820 2
7098.2.bk $$\chi_{7098}(4393, \cdot)$$ n/a 408 2
7098.2.bm $$\chi_{7098}(823, \cdot)$$ n/a 412 2
7098.2.bn $$\chi_{7098}(4541, \cdot)$$ n/a 820 2
7098.2.bq $$\chi_{7098}(3233, \cdot)$$ n/a 824 2
7098.2.bu $$\chi_{7098}(995, \cdot)$$ n/a 1232 4
7098.2.bv $$\chi_{7098}(1451, \cdot)$$ n/a 1648 4
7098.2.bw $$\chi_{7098}(695, \cdot)$$ n/a 1640 4
7098.2.bx $$\chi_{7098}(1441, \cdot)$$ n/a 816 4
7098.2.by $$\chi_{7098}(19, \cdot)$$ n/a 824 4
7098.2.bz $$\chi_{7098}(577, \cdot)$$ n/a 816 4
7098.2.cg $$\chi_{7098}(1333, \cdot)$$ n/a 824 4
7098.2.ch $$\chi_{7098}(3131, \cdot)$$ n/a 1640 4
7098.2.ci $$\chi_{7098}(547, \cdot)$$ n/a 2208 12
7098.2.ck $$\chi_{7098}(209, \cdot)$$ n/a 5856 12
7098.2.cm $$\chi_{7098}(545, \cdot)$$ n/a 5856 12
7098.2.co $$\chi_{7098}(883, \cdot)$$ n/a 2160 12
7098.2.cq $$\chi_{7098}(211, \cdot)$$ n/a 4416 24
7098.2.cr $$\chi_{7098}(373, \cdot)$$ n/a 5808 24
7098.2.cs $$\chi_{7098}(289, \cdot)$$ n/a 5808 24
7098.2.ct $$\chi_{7098}(79, \cdot)$$ n/a 5856 24
7098.2.cu $$\chi_{7098}(265, \cdot)$$ n/a 5760 24
7098.2.cv $$\chi_{7098}(281, \cdot)$$ n/a 8736 24
7098.2.cz $$\chi_{7098}(419, \cdot)$$ n/a 11616 24
7098.2.dc $$\chi_{7098}(101, \cdot)$$ n/a 11664 24
7098.2.dd $$\chi_{7098}(205, \cdot)$$ n/a 5808 24
7098.2.df $$\chi_{7098}(25, \cdot)$$ n/a 5856 24
7098.2.dh $$\chi_{7098}(17, \cdot)$$ n/a 11664 24
7098.2.dj $$\chi_{7098}(311, \cdot)$$ n/a 11616 24
7098.2.dm $$\chi_{7098}(121, \cdot)$$ n/a 5808 24
7098.2.do $$\chi_{7098}(269, \cdot)$$ n/a 11664 24
7098.2.dq $$\chi_{7098}(131, \cdot)$$ n/a 11616 24
7098.2.dv $$\chi_{7098}(185, \cdot)$$ n/a 11664 24
7098.2.dx $$\chi_{7098}(43, \cdot)$$ n/a 4320 24
7098.2.dz $$\chi_{7098}(251, \cdot)$$ n/a 11616 24
7098.2.ea $$\chi_{7098}(145, \cdot)$$ n/a 11616 48
7098.2.eb $$\chi_{7098}(137, \cdot)$$ n/a 23328 48
7098.2.ei $$\chi_{7098}(11, \cdot)$$ n/a 23328 48
7098.2.ej $$\chi_{7098}(317, \cdot)$$ n/a 23232 48
7098.2.ek $$\chi_{7098}(71, \cdot)$$ n/a 17472 48
7098.2.el $$\chi_{7098}(31, \cdot)$$ n/a 11712 48
7098.2.em $$\chi_{7098}(115, \cdot)$$ n/a 11616 48
7098.2.en $$\chi_{7098}(97, \cdot)$$ n/a 11712 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7098))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7098)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(338))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(507))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(546))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1014))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1183))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2366))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3549))$$$$^{\oplus 2}$$