# Properties

 Label 8112.2 Level 8112 Weight 2 Dimension 755699 Nonzero newspaces 56 Sturm bound 7268352

## Defining parameters

 Level: $$N$$ = $$8112 = 2^{4} \cdot 3 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$56$$ Sturm bound: $$7268352$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8112))$$.

Total New Old
Modular forms 1829856 759379 1070477
Cusp forms 1804321 755699 1048622
Eisenstein series 25535 3680 21855

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8112))$$

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
8112.2.a $$\chi_{8112}(1, \cdot)$$ 8112.2.a.a 1 1
8112.2.a.b 1
8112.2.a.c 1
8112.2.a.d 1
8112.2.a.e 1
8112.2.a.f 1
8112.2.a.g 1
8112.2.a.h 1
8112.2.a.i 1
8112.2.a.j 1
8112.2.a.k 1
8112.2.a.l 1
8112.2.a.m 1
8112.2.a.n 1
8112.2.a.o 1
8112.2.a.p 1
8112.2.a.q 1
8112.2.a.r 1
8112.2.a.s 1
8112.2.a.t 1
8112.2.a.u 1
8112.2.a.v 1
8112.2.a.w 1
8112.2.a.x 1
8112.2.a.y 1
8112.2.a.z 1
8112.2.a.ba 1
8112.2.a.bb 1
8112.2.a.bc 1
8112.2.a.bd 1
8112.2.a.be 1
8112.2.a.bf 1
8112.2.a.bg 1
8112.2.a.bh 1
8112.2.a.bi 1
8112.2.a.bj 2
8112.2.a.bk 2
8112.2.a.bl 2
8112.2.a.bm 2
8112.2.a.bn 2
8112.2.a.bo 2
8112.2.a.bp 2
8112.2.a.bq 2
8112.2.a.br 2
8112.2.a.bs 2
8112.2.a.bt 2
8112.2.a.bu 2
8112.2.a.bv 2
8112.2.a.bw 2
8112.2.a.bx 2
8112.2.a.by 3
8112.2.a.bz 3
8112.2.a.ca 3
8112.2.a.cb 3
8112.2.a.cc 3
8112.2.a.cd 3
8112.2.a.ce 3
8112.2.a.cf 3
8112.2.a.cg 3
8112.2.a.ch 3
8112.2.a.ci 3
8112.2.a.cj 3
8112.2.a.ck 3
8112.2.a.cl 3
8112.2.a.cm 3
8112.2.a.cn 3
8112.2.a.co 3
8112.2.a.cp 3
8112.2.a.cq 4
8112.2.a.cr 4
8112.2.a.cs 4
8112.2.a.ct 6
8112.2.a.cu 6
8112.2.a.cv 6
8112.2.a.cw 6
8112.2.c $$\chi_{8112}(337, \cdot)$$ n/a 154 1
8112.2.d $$\chi_{8112}(7775, \cdot)$$ n/a 310 1
8112.2.g $$\chi_{8112}(4057, \cdot)$$ None 0 1
8112.2.h $$\chi_{8112}(4055, \cdot)$$ None 0 1
8112.2.j $$\chi_{8112}(3719, \cdot)$$ None 0 1
8112.2.m $$\chi_{8112}(4393, \cdot)$$ None 0 1
8112.2.n $$\chi_{8112}(8111, \cdot)$$ n/a 308 1
8112.2.q $$\chi_{8112}(529, \cdot)$$ n/a 308 2
8112.2.r $$\chi_{8112}(3619, \cdot)$$ n/a 1232 2
8112.2.u $$\chi_{8112}(1253, \cdot)$$ n/a 2424 2
8112.2.v $$\chi_{8112}(2027, \cdot)$$ n/a 2424 2
8112.2.x $$\chi_{8112}(2029, \cdot)$$ n/a 1240 2
8112.2.bb $$\chi_{8112}(775, \cdot)$$ None 0 2
8112.2.bc $$\chi_{8112}(4831, \cdot)$$ n/a 308 2
8112.2.bf $$\chi_{8112}(2465, \cdot)$$ n/a 596 2
8112.2.bg $$\chi_{8112}(6521, \cdot)$$ None 0 2
8112.2.bh $$\chi_{8112}(1691, \cdot)$$ n/a 2436 2
8112.2.bj $$\chi_{8112}(2365, \cdot)$$ n/a 1232 2
8112.2.bm $$\chi_{8112}(437, \cdot)$$ n/a 2424 2
8112.2.bn $$\chi_{8112}(2803, \cdot)$$ n/a 1232 2
8112.2.bq $$\chi_{8112}(23, \cdot)$$ None 0 2
8112.2.br $$\chi_{8112}(4585, \cdot)$$ None 0 2
8112.2.bu $$\chi_{8112}(191, \cdot)$$ n/a 616 2
8112.2.bv $$\chi_{8112}(4417, \cdot)$$ n/a 308 2
8112.2.bz $$\chi_{8112}(4079, \cdot)$$ n/a 616 2
8112.2.ca $$\chi_{8112}(361, \cdot)$$ None 0 2
8112.2.cd $$\chi_{8112}(4247, \cdot)$$ None 0 2
8112.2.ce $$\chi_{8112}(5765, \cdot)$$ n/a 4848 4
8112.2.ch $$\chi_{8112}(19, \cdot)$$ n/a 2464 4
8112.2.cj $$\chi_{8112}(1837, \cdot)$$ n/a 2464 4
8112.2.cl $$\chi_{8112}(1667, \cdot)$$ n/a 4848 4
8112.2.cm $$\chi_{8112}(89, \cdot)$$ None 0 4
8112.2.cn $$\chi_{8112}(1601, \cdot)$$ n/a 1192 4
8112.2.cq $$\chi_{8112}(319, \cdot)$$ n/a 616 4
8112.2.cr $$\chi_{8112}(2455, \cdot)$$ None 0 4
8112.2.cv $$\chi_{8112}(2005, \cdot)$$ n/a 2464 4
8112.2.cx $$\chi_{8112}(1499, \cdot)$$ n/a 4848 4
8112.2.cz $$\chi_{8112}(4075, \cdot)$$ n/a 2464 4
8112.2.da $$\chi_{8112}(1709, \cdot)$$ n/a 4848 4
8112.2.dc $$\chi_{8112}(625, \cdot)$$ n/a 2184 12
8112.2.df $$\chi_{8112}(623, \cdot)$$ n/a 4368 12
8112.2.dg $$\chi_{8112}(25, \cdot)$$ None 0 12
8112.2.dj $$\chi_{8112}(599, \cdot)$$ None 0 12
8112.2.dl $$\chi_{8112}(311, \cdot)$$ None 0 12
8112.2.dm $$\chi_{8112}(313, \cdot)$$ None 0 12
8112.2.dp $$\chi_{8112}(287, \cdot)$$ n/a 4368 12
8112.2.dq $$\chi_{8112}(961, \cdot)$$ n/a 2184 12
8112.2.ds $$\chi_{8112}(289, \cdot)$$ n/a 4368 24
8112.2.du $$\chi_{8112}(187, \cdot)$$ n/a 17472 24
8112.2.dv $$\chi_{8112}(317, \cdot)$$ n/a 34848 24
8112.2.dx $$\chi_{8112}(181, \cdot)$$ n/a 17472 24
8112.2.dz $$\chi_{8112}(131, \cdot)$$ n/a 34848 24
8112.2.ed $$\chi_{8112}(281, \cdot)$$ None 0 24
8112.2.ee $$\chi_{8112}(161, \cdot)$$ n/a 8688 24
8112.2.eh $$\chi_{8112}(31, \cdot)$$ n/a 4368 24
8112.2.ei $$\chi_{8112}(151, \cdot)$$ None 0 24
8112.2.ej $$\chi_{8112}(157, \cdot)$$ n/a 17472 24
8112.2.el $$\chi_{8112}(155, \cdot)$$ n/a 34848 24
8112.2.en $$\chi_{8112}(5, \cdot)$$ n/a 34848 24
8112.2.eq $$\chi_{8112}(499, \cdot)$$ n/a 17472 24
8112.2.er $$\chi_{8112}(263, \cdot)$$ None 0 24
8112.2.eu $$\chi_{8112}(121, \cdot)$$ None 0 24
8112.2.ev $$\chi_{8112}(95, \cdot)$$ n/a 8736 24
8112.2.ez $$\chi_{8112}(49, \cdot)$$ n/a 4368 24
8112.2.fa $$\chi_{8112}(575, \cdot)$$ n/a 8736 24
8112.2.fd $$\chi_{8112}(217, \cdot)$$ None 0 24
8112.2.fe $$\chi_{8112}(407, \cdot)$$ None 0 24
8112.2.fh $$\chi_{8112}(245, \cdot)$$ n/a 69696 48
8112.2.fi $$\chi_{8112}(115, \cdot)$$ n/a 34944 48
8112.2.fl $$\chi_{8112}(179, \cdot)$$ n/a 69696 48
8112.2.fn $$\chi_{8112}(61, \cdot)$$ n/a 34944 48
8112.2.fo $$\chi_{8112}(7, \cdot)$$ None 0 48
8112.2.fp $$\chi_{8112}(175, \cdot)$$ n/a 8736 48
8112.2.fs $$\chi_{8112}(305, \cdot)$$ n/a 17376 48
8112.2.ft $$\chi_{8112}(41, \cdot)$$ None 0 48
8112.2.fx $$\chi_{8112}(35, \cdot)$$ n/a 69696 48
8112.2.fz $$\chi_{8112}(205, \cdot)$$ n/a 34944 48
8112.2.ga $$\chi_{8112}(67, \cdot)$$ n/a 34944 48
8112.2.gd $$\chi_{8112}(149, \cdot)$$ n/a 69696 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8112))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8112)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(338))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(507))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(624))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(676))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1014))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1352))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2028))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2704))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4056))$$$$^{\oplus 2}$$