Space of modular forms of level 5850 and weight 2

• Label: 5850.2
• Level: 5850
• Weight: 2
• Dimension: 218021
• Nonzero newspaces: 100
• Sturm bound: 3628800

Defining parameters

Level:	$N$	=	$5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13$
Weight:	$k$	=	$2$
Nonzero newspaces:			$100$
Sturm bound:			$3628800$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(5850))$.

	Total	New	Old
Modular forms	917952	218021	699931
Cusp forms	896449	218021	678428
Eisenstein series	21503	0	21503

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(5850))$

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
5850.2.a	$\chi_{5850}(1, \cdot)$	5850.2.a.a	1	1
		5850.2.a.b	1
		5850.2.a.c	1
		5850.2.a.d	1
		5850.2.a.e	1
		5850.2.a.f	1
		5850.2.a.g	1
		5850.2.a.h	1
		5850.2.a.i	1
		5850.2.a.j	1
		5850.2.a.k	1
		5850.2.a.l	1
		5850.2.a.m	1
		5850.2.a.n	1
		5850.2.a.o	1
		5850.2.a.p	1
		5850.2.a.q	1
		5850.2.a.r	1
		5850.2.a.s	1
		5850.2.a.t	1
		5850.2.a.u	1
		5850.2.a.v	1
		5850.2.a.w	1
		5850.2.a.x	1
		5850.2.a.y	1
		5850.2.a.z	1
		5850.2.a.ba	1
		5850.2.a.bb	1
		5850.2.a.bc	1
		5850.2.a.bd	1
		5850.2.a.be	1
		5850.2.a.bf	1
		5850.2.a.bg	1
		5850.2.a.bh	1
		5850.2.a.bi	1
		5850.2.a.bj	1
		5850.2.a.bk	1
		5850.2.a.bl	1
		5850.2.a.bm	1
		5850.2.a.bn	1
		5850.2.a.bo	1
		5850.2.a.bp	1
		5850.2.a.bq	1
		5850.2.a.br	1
		5850.2.a.bs	1
		5850.2.a.bt	1
		5850.2.a.bu	1
		5850.2.a.bv	1
		5850.2.a.bw	1
		5850.2.a.bx	1
		5850.2.a.by	1
		5850.2.a.bz	1
		5850.2.a.ca	1
		5850.2.a.cb	1
		5850.2.a.cc	1
		5850.2.a.cd	2
		5850.2.a.ce	2
		5850.2.a.cf	2
		5850.2.a.cg	2
		5850.2.a.ch	2
		5850.2.a.ci	2
		5850.2.a.cj	2
		5850.2.a.ck	2
		5850.2.a.cl	2
5850.2.a.cm	2
5850.2.a.cn	2
5850.2.a.co	3
5850.2.a.cp	3
5850.2.a.cq	3
5850.2.a.cr	3
5850.2.a.cs	3
5850.2.a.ct	3
5850.2.b	$\chi_{5850}(1351, \cdot)$	n/a	110	1
5850.2.e	$\chi_{5850}(5149, \cdot)$	5850.2.e.a	2	1
		5850.2.e.b	2
		5850.2.e.c	2
		5850.2.e.d	2
		5850.2.e.e	2
		5850.2.e.f	2
		5850.2.e.g	2
		5850.2.e.h	2
		5850.2.e.i	2
		5850.2.e.j	2
		5850.2.e.k	2
		5850.2.e.l	2
		5850.2.e.m	2
		5850.2.e.n	2
		5850.2.e.o	2
		5850.2.e.p	2
		5850.2.e.q	2
		5850.2.e.r	2
		5850.2.e.s	2
		5850.2.e.t	2
		5850.2.e.u	2
		5850.2.e.v	2
		5850.2.e.w	2
		5850.2.e.x	2
		5850.2.e.y	2
		5850.2.e.z	2
		5850.2.e.ba	2
		5850.2.e.bb	2
		5850.2.e.bc	2
		5850.2.e.bd	2
		5850.2.e.be	2
		5850.2.e.bf	2
		5850.2.e.bg	2
		5850.2.e.bh	4
		5850.2.e.bi	4
		5850.2.e.bj	4
		5850.2.e.bk	4
		5850.2.e.bl	4
		5850.2.e.bm	4
5850.2.f	$\chi_{5850}(649, \cdot)$	n/a	104	1
5850.2.i	$\chi_{5850}(451, \cdot)$	n/a	222	2
5850.2.j	$\chi_{5850}(1951, \cdot)$	n/a	456	2
5850.2.k	$\chi_{5850}(601, \cdot)$	n/a	532	2
5850.2.l	$\chi_{5850}(2401, \cdot)$	n/a	532	2
5850.2.m	$\chi_{5850}(1243, \cdot)$	n/a	210	2
5850.2.o	$\chi_{5850}(1457, \cdot)$	n/a	144	2
5850.2.q	$\chi_{5850}(1799, \cdot)$	n/a	168	2
5850.2.s	$\chi_{5850}(2501, \cdot)$	n/a	172	2
5850.2.v	$\chi_{5850}(2807, \cdot)$	n/a	168	2
5850.2.w	$\chi_{5850}(307, \cdot)$	n/a	210	2
5850.2.y	$\chi_{5850}(1171, \cdot)$	n/a	600	4
5850.2.z	$\chi_{5850}(1699, \cdot)$	n/a	504	2
5850.2.bc	$\chi_{5850}(751, \cdot)$	n/a	532	2
5850.2.be	$\chi_{5850}(3949, \cdot)$	n/a	504	2
5850.2.bh	$\chi_{5850}(2599, \cdot)$	n/a	504	2
5850.2.bk	$\chi_{5850}(199, \cdot)$	n/a	208	2
5850.2.bn	$\chi_{5850}(4651, \cdot)$	n/a	532	2
5850.2.bp	$\chi_{5850}(1249, \cdot)$	n/a	432	2
5850.2.bq	$\chi_{5850}(3799, \cdot)$	n/a	212	2
5850.2.bt	$\chi_{5850}(901, \cdot)$	n/a	224	2
5850.2.bu	$\chi_{5850}(3301, \cdot)$	n/a	532	2
5850.2.bw	$\chi_{5850}(3649, \cdot)$	n/a	504	2
5850.2.ca	$\chi_{5850}(49, \cdot)$	n/a	504	2
5850.2.cb	$\chi_{5850}(469, \cdot)$	n/a	600	4
5850.2.ce	$\chi_{5850}(181, \cdot)$	n/a	696	4
5850.2.ch	$\chi_{5850}(1819, \cdot)$	n/a	704	4
5850.2.cj	$\chi_{5850}(193, \cdot)$	n/a	1008	4
5850.2.ck	$\chi_{5850}(643, \cdot)$	n/a	1008	4
5850.2.cn	$\chi_{5850}(1207, \cdot)$	n/a	420	4
5850.2.co	$\chi_{5850}(2257, \cdot)$	n/a	1008	4
5850.2.cr	$\chi_{5850}(3857, \cdot)$	n/a	1008	4
5850.2.ct	$\chi_{5850}(2357, \cdot)$	n/a	336	4
5850.2.cu	$\chi_{5850}(257, \cdot)$	n/a	1008	4
5850.2.cx	$\chi_{5850}(857, \cdot)$	n/a	1008	4
5850.2.cz	$\chi_{5850}(749, \cdot)$	n/a	1008	4
5850.2.da	$\chi_{5850}(851, \cdot)$	n/a	1064	4
5850.2.dc	$\chi_{5850}(1151, \cdot)$	n/a	360	4
5850.2.df	$\chi_{5850}(401, \cdot)$	n/a	1064	4
5850.2.dh	$\chi_{5850}(2099, \cdot)$	n/a	1008	4
5850.2.di	$\chi_{5850}(149, \cdot)$	n/a	1008	4
5850.2.dk	$\chi_{5850}(449, \cdot)$	n/a	336	4
5850.2.dn	$\chi_{5850}(551, \cdot)$	n/a	1064	4
5850.2.do	$\chi_{5850}(443, \cdot)$	n/a	864	4
5850.2.dr	$\chi_{5850}(893, \cdot)$	n/a	1008	4
5850.2.ds	$\chi_{5850}(107, \cdot)$	n/a	336	4
5850.2.du	$\chi_{5850}(2207, \cdot)$	n/a	1008	4
5850.2.dw	$\chi_{5850}(457, \cdot)$	n/a	1008	4
5850.2.dz	$\chi_{5850}(1357, \cdot)$	n/a	1008	4
5850.2.ea	$\chi_{5850}(1657, \cdot)$	n/a	420	4
5850.2.ed	$\chi_{5850}(7, \cdot)$	n/a	1008	4
5850.2.ee	$\chi_{5850}(841, \cdot)$	n/a	3360	8
5850.2.ef	$\chi_{5850}(391, \cdot)$	n/a	2880	8
5850.2.eg	$\chi_{5850}(991, \cdot)$	n/a	1408	8
5850.2.eh	$\chi_{5850}(61, \cdot)$	n/a	3360	8
5850.2.ej	$\chi_{5850}(73, \cdot)$	n/a	1400	8
5850.2.ek	$\chi_{5850}(233, \cdot)$	n/a	1120	8
5850.2.en	$\chi_{5850}(161, \cdot)$	n/a	1120	8
5850.2.ep	$\chi_{5850}(359, \cdot)$	n/a	1120	8
5850.2.er	$\chi_{5850}(53, \cdot)$	n/a	960	8
5850.2.et	$\chi_{5850}(1477, \cdot)$	n/a	1400	8
5850.2.eu	$\chi_{5850}(511, \cdot)$	n/a	3360	8
5850.2.ex	$\chi_{5850}(529, \cdot)$	n/a	3360	8
5850.2.ez	$\chi_{5850}(829, \cdot)$	n/a	1408	8
5850.2.fc	$\chi_{5850}(259, \cdot)$	n/a	3360	8
5850.2.ff	$\chi_{5850}(439, \cdot)$	n/a	3360	8
5850.2.fi	$\chi_{5850}(139, \cdot)$	n/a	3360	8
5850.2.fk	$\chi_{5850}(571, \cdot)$	n/a	3360	8
5850.2.fl	$\chi_{5850}(361, \cdot)$	n/a	1392	8
5850.2.fo	$\chi_{5850}(289, \cdot)$	n/a	1392	8
5850.2.fp	$\chi_{5850}(79, \cdot)$	n/a	2880	8
5850.2.fr	$\chi_{5850}(121, \cdot)$	n/a	3360	8
5850.2.ft	$\chi_{5850}(979, \cdot)$	n/a	3360	8
5850.2.fw	$\chi_{5850}(67, \cdot)$	n/a	6720	16
5850.2.fz	$\chi_{5850}(697, \cdot)$	n/a	6720	16
5850.2.ga	$\chi_{5850}(37, \cdot)$	n/a	2800	16
5850.2.gd	$\chi_{5850}(223, \cdot)$	n/a	6720	16
5850.2.gf	$\chi_{5850}(563, \cdot)$	n/a	6720	16
5850.2.gh	$\chi_{5850}(503, \cdot)$	n/a	2240	16
5850.2.gi	$\chi_{5850}(653, \cdot)$	n/a	6720	16
5850.2.gl	$\chi_{5850}(677, \cdot)$	n/a	5760	16
5850.2.gm	$\chi_{5850}(281, \cdot)$	n/a	6720	16
5850.2.gp	$\chi_{5850}(89, \cdot)$	n/a	2240	16
5850.2.gr	$\chi_{5850}(59, \cdot)$	n/a	6720	16
5850.2.gs	$\chi_{5850}(509, \cdot)$	n/a	6720	16
5850.2.gu	$\chi_{5850}(41, \cdot)$	n/a	6720	16
5850.2.gx	$\chi_{5850}(71, \cdot)$	n/a	2240	16
5850.2.gz	$\chi_{5850}(11, \cdot)$	n/a	6720	16
5850.2.ha	$\chi_{5850}(239, \cdot)$	n/a	6720	16
5850.2.hc	$\chi_{5850}(77, \cdot)$	n/a	6720	16
5850.2.hf	$\chi_{5850}(23, \cdot)$	n/a	6720	16
5850.2.hg	$\chi_{5850}(17, \cdot)$	n/a	2240	16
5850.2.hi	$\chi_{5850}(113, \cdot)$	n/a	6720	16
5850.2.hl	$\chi_{5850}(163, \cdot)$	n/a	2800	16
5850.2.hm	$\chi_{5850}(187, \cdot)$	n/a	6720	16
5850.2.hp	$\chi_{5850}(553, \cdot)$	n/a	6720	16
5850.2.hq	$\chi_{5850}(427, \cdot)$	n/a	6720	16

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(5850))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(5850)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 36}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(234))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(325))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(390))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(450))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(585))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(650))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(975))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1170))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1950))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2925))$$^{\oplus 2}$