Space of modular forms of level 4675 and weight 2

• Label: 4675.2
• Level: 4675
• Weight: 2
• Dimension: 772072
• Nonzero newspaces: 126
• Sturm bound: 3456000

Defining parameters

Level:	$N$	=	$4675 = 5^{2} \cdot 11 \cdot 17$
Weight:	$k$	=	$2$
Nonzero newspaces:			$126$
Sturm bound:			$3456000$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(4675))$.

	Total	New	Old
Modular forms	872960	783144	89816
Cusp forms	855041	772072	82969
Eisenstein series	17919	11072	6847

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(4675))$

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
4675.2.a	$\chi_{4675}(1, \cdot)$	4675.2.a.a	1	1
		4675.2.a.b	1
		4675.2.a.c	1
		4675.2.a.d	1
		4675.2.a.e	1
		4675.2.a.f	1
		4675.2.a.g	1
		4675.2.a.h	1
		4675.2.a.i	1
		4675.2.a.j	1
		4675.2.a.k	1
		4675.2.a.l	1
		4675.2.a.m	1
		4675.2.a.n	1
		4675.2.a.o	1
		4675.2.a.p	1
		4675.2.a.q	1
		4675.2.a.r	1
		4675.2.a.s	1
		4675.2.a.t	1
		4675.2.a.u	2
		4675.2.a.v	2
		4675.2.a.w	3
		4675.2.a.x	3
		4675.2.a.y	3
		4675.2.a.z	3
		4675.2.a.ba	3
		4675.2.a.bb	3
		4675.2.a.bc	3
		4675.2.a.bd	4
		4675.2.a.be	4
		4675.2.a.bf	5
		4675.2.a.bg	5
		4675.2.a.bh	6
		4675.2.a.bi	9
		4675.2.a.bj	11
		4675.2.a.bk	11
		4675.2.a.bl	11
		4675.2.a.bm	11
		4675.2.a.bn	12
		4675.2.a.bo	12
		4675.2.a.bp	13
		4675.2.a.bq	13
		4675.2.a.br	18
		4675.2.a.bs	18
		4675.2.a.bt	22
		4675.2.a.bu	22
4675.2.b	$\chi_{4675}(749, \cdot)$	n/a	240	1
4675.2.e	$\chi_{4675}(2124, \cdot)$	n/a	272	1
4675.2.f	$\chi_{4675}(1376, \cdot)$	n/a	284	1
4675.2.i	$\chi_{4675}(276, \cdot)$	n/a	568	2
4675.2.l	$\chi_{4675}(582, \cdot)$	n/a	640	2
4675.2.m	$\chi_{4675}(307, \cdot)$	n/a	576	2
4675.2.p	$\chi_{4675}(1682, \cdot)$	n/a	640	2
4675.2.q	$\chi_{4675}(1143, \cdot)$	n/a	640	2
4675.2.s	$\chi_{4675}(1024, \cdot)$	n/a	544	2
4675.2.u	$\chi_{4675}(86, \cdot)$	n/a	1920	4
4675.2.v	$\chi_{4675}(851, \cdot)$	n/a	1216	4
4675.2.w	$\chi_{4675}(936, \cdot)$	n/a	1600	4
4675.2.x	$\chi_{4675}(511, \cdot)$	n/a	1920	4
4675.2.y	$\chi_{4675}(1021, \cdot)$	n/a	1920	4
4675.2.z	$\chi_{4675}(1191, \cdot)$	n/a	1920	4
4675.2.bb	$\chi_{4675}(593, \cdot)$	n/a	1280	4
4675.2.bc	$\chi_{4675}(1651, \cdot)$	n/a	1144	4
4675.2.be	$\chi_{4675}(474, \cdot)$	n/a	1072	4
4675.2.bh	$\chi_{4675}(32, \cdot)$	n/a	1280	4
4675.2.bi	$\chi_{4675}(509, \cdot)$	n/a	2144	4
4675.2.bl	$\chi_{4675}(664, \cdot)$	n/a	1920	4
4675.2.bn	$\chi_{4675}(1291, \cdot)$	n/a	2144	4
4675.2.bt	$\chi_{4675}(356, \cdot)$	n/a	2144	4
4675.2.bu	$\chi_{4675}(441, \cdot)$	n/a	1808	4
4675.2.bx	$\chi_{4675}(526, \cdot)$	n/a	1344	4
4675.2.by	$\chi_{4675}(16, \cdot)$	n/a	2144	4
4675.2.cc	$\chi_{4675}(1939, \cdot)$	n/a	1920	4
4675.2.cd	$\chi_{4675}(169, \cdot)$	n/a	2144	4
4675.2.cg	$\chi_{4675}(339, \cdot)$	n/a	2144	4
4675.2.ch	$\chi_{4675}(1274, \cdot)$	n/a	1280	4
4675.2.ck	$\chi_{4675}(254, \cdot)$	n/a	1792	4
4675.2.cl	$\chi_{4675}(1684, \cdot)$	n/a	1600	4
4675.2.co	$\chi_{4675}(324, \cdot)$	n/a	1152	4
4675.2.cp	$\chi_{4675}(69, \cdot)$	n/a	1920	4
4675.2.cs	$\chi_{4675}(834, \cdot)$	n/a	1920	4
4675.2.ct	$\chi_{4675}(3314, \cdot)$	n/a	2144	4
4675.2.cx	$\chi_{4675}(2566, \cdot)$	n/a	2144	4
4675.2.cz	$\chi_{4675}(232, \cdot)$	n/a	2160	8
4675.2.da	$\chi_{4675}(351, \cdot)$	n/a	2688	8
4675.2.dd	$\chi_{4675}(549, \cdot)$	n/a	2560	8
4675.2.de	$\chi_{4675}(507, \cdot)$	n/a	2160	8
4675.2.dg	$\chi_{4675}(1466, \cdot)$	n/a	4288	8
4675.2.dj	$\chi_{4675}(2214, \cdot)$	n/a	4288	8
4675.2.dl	$\chi_{4675}(89, \cdot)$	n/a	3584	8
4675.2.dp	$\chi_{4675}(489, \cdot)$	n/a	4288	8
4675.2.dq	$\chi_{4675}(4, \cdot)$	n/a	4288	8
4675.2.dr	$\chi_{4675}(174, \cdot)$	n/a	2560	8
4675.2.ds	$\chi_{4675}(327, \cdot)$	n/a	4288	8
4675.2.dv	$\chi_{4675}(888, \cdot)$	n/a	4288	8
4675.2.dw	$\chi_{4675}(208, \cdot)$	n/a	4288	8
4675.2.ea	$\chi_{4675}(293, \cdot)$	n/a	2560	8
4675.2.eb	$\chi_{4675}(387, \cdot)$	n/a	4288	8
4675.2.ec	$\chi_{4675}(123, \cdot)$	n/a	4288	8
4675.2.ee	$\chi_{4675}(1172, \cdot)$	n/a	4288	8
4675.2.eh	$\chi_{4675}(613, \cdot)$	n/a	3840	8
4675.2.ei	$\chi_{4675}(392, \cdot)$	n/a	3840	8
4675.2.ek	$\chi_{4675}(1427, \cdot)$	n/a	4288	8
4675.2.em	$\chi_{4675}(118, \cdot)$	n/a	2560	8
4675.2.en	$\chi_{4675}(373, \cdot)$	n/a	4288	8
4675.2.eo	$\chi_{4675}(237, \cdot)$	n/a	4288	8
4675.2.et	$\chi_{4675}(52, \cdot)$	n/a	3840	8
4675.2.ex	$\chi_{4675}(18, \cdot)$	n/a	2304	8
4675.2.ey	$\chi_{4675}(953, \cdot)$	n/a	3840	8
4675.2.ez	$\chi_{4675}(1242, \cdot)$	n/a	3840	8
4675.2.fb	$\chi_{4675}(288, \cdot)$	n/a	4288	8
4675.2.fc	$\chi_{4675}(72, \cdot)$	n/a	4288	8
4675.2.ff	$\chi_{4675}(948, \cdot)$	n/a	4288	8
4675.2.fg	$\chi_{4675}(13, \cdot)$	n/a	4288	8
4675.2.fh	$\chi_{4675}(1007, \cdot)$	n/a	2560	8
4675.2.fl	$\chi_{4675}(98, \cdot)$	n/a	4288	8
4675.2.fn	$\chi_{4675}(633, \cdot)$	n/a	4288	8
4675.2.fp	$\chi_{4675}(191, \cdot)$	n/a	4288	8
4675.2.ft	$\chi_{4675}(81, \cdot)$	n/a	4288	8
4675.2.fu	$\chi_{4675}(361, \cdot)$	n/a	4288	8
4675.2.fv	$\chi_{4675}(251, \cdot)$	n/a	2688	8
4675.2.fx	$\chi_{4675}(166, \cdot)$	n/a	3616	8
4675.2.fy	$\chi_{4675}(234, \cdot)$	n/a	4288	8
4675.2.ga	$\chi_{4675}(162, \cdot)$	n/a	8576	16
4675.2.gd	$\chi_{4675}(178, \cdot)$	n/a	8576	16
4675.2.ge	$\chi_{4675}(87, \cdot)$	n/a	8576	16
4675.2.gf	$\chi_{4675}(117, \cdot)$	n/a	8576	16
4675.2.gg	$\chi_{4675}(2, \cdot)$	n/a	8576	16
4675.2.gl	$\chi_{4675}(457, \cdot)$	n/a	5120	16
4675.2.gn	$\chi_{4675}(104, \cdot)$	n/a	8576	16
4675.2.gp	$\chi_{4675}(366, \cdot)$	n/a	8576	16
4675.2.gr	$\chi_{4675}(36, \cdot)$	n/a	8576	16
4675.2.gt	$\chi_{4675}(144, \cdot)$	n/a	7232	16
4675.2.gu	$\chi_{4675}(49, \cdot)$	n/a	5120	16
4675.2.gx	$\chi_{4675}(9, \cdot)$	n/a	8576	16
4675.2.gy	$\chi_{4675}(434, \cdot)$	n/a	8576	16
4675.2.ha	$\chi_{4675}(26, \cdot)$	n/a	5376	16
4675.2.hd	$\chi_{4675}(246, \cdot)$	n/a	8576	16
4675.2.he	$\chi_{4675}(236, \cdot)$	n/a	8576	16
4675.2.hh	$\chi_{4675}(111, \cdot)$	n/a	7168	16
4675.2.hj	$\chi_{4675}(59, \cdot)$	n/a	8576	16
4675.2.hl	$\chi_{4675}(138, \cdot)$	n/a	8576	16
4675.2.hm	$\chi_{4675}(127, \cdot)$	n/a	8576	16
4675.2.hn	$\chi_{4675}(83, \cdot)$	n/a	8576	16
4675.2.ho	$\chi_{4675}(417, \cdot)$	n/a	8576	16
4675.2.ht	$\chi_{4675}(332, \cdot)$	n/a	5120	16
4675.2.hu	$\chi_{4675}(348, \cdot)$	n/a	8576	16
4675.2.hw	$\chi_{4675}(258, \cdot)$	n/a	17152	32
4675.2.hy	$\chi_{4675}(108, \cdot)$	n/a	17152	32
4675.2.ie	$\chi_{4675}(12, \cdot)$	n/a	14400	32
4675.2.if	$\chi_{4675}(82, \cdot)$	n/a	10240	32
4675.2.ig	$\chi_{4675}(163, \cdot)$	n/a	17152	32
4675.2.ih	$\chi_{4675}(58, \cdot)$	n/a	17152	32
4675.2.ii	$\chi_{4675}(139, \cdot)$	n/a	17152	32
4675.2.il	$\chi_{4675}(41, \cdot)$	n/a	17152	32
4675.2.in	$\chi_{4675}(131, \cdot)$	n/a	17152	32
4675.2.ip	$\chi_{4675}(79, \cdot)$	n/a	17152	32
4675.2.iq	$\chi_{4675}(29, \cdot)$	n/a	17152	32
4675.2.it	$\chi_{4675}(24, \cdot)$	n/a	10240	32
4675.2.iu	$\chi_{4675}(39, \cdot)$	n/a	17152	32
4675.2.ix	$\chi_{4675}(61, \cdot)$	n/a	17152	32
4675.2.iy	$\chi_{4675}(226, \cdot)$	n/a	10752	32
4675.2.jb	$\chi_{4675}(6, \cdot)$	n/a	17152	32
4675.2.jc	$\chi_{4675}(116, \cdot)$	n/a	17152	32
4675.2.je	$\chi_{4675}(54, \cdot)$	n/a	17152	32
4675.2.jh	$\chi_{4675}(48, \cdot)$	n/a	17152	32
4675.2.ji	$\chi_{4675}(147, \cdot)$	n/a	17152	32
4675.2.jj	$\chi_{4675}(218, \cdot)$	n/a	10240	32
4675.2.jk	$\chi_{4675}(133, \cdot)$	n/a	14400	32
4675.2.jl	$\chi_{4675}(3, \cdot)$	n/a	17152	32
4675.2.jr	$\chi_{4675}(37, \cdot)$	n/a	17152	32

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(4675))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(4675)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(85))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(187))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(425))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(935))$$^{\oplus 2}$