Space of modular forms of level 8112 and weight 2

• 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 available 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(1))$$^{\oplus 30}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 15}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$^{\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}$