Space of modular forms of level 4140 and weight 2

• Label: 4140.2
• Level: 4140
• Weight: 2
• Dimension: 191254
• Nonzero newspaces: 48
• Sturm bound: 1824768

Defining parameters

Level:	$N$	=	$4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23$
Weight:	$k$	=	$2$
Nonzero newspaces:			$48$
Sturm bound:			$1824768$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(4140))$.

	Total	New	Old
Modular forms	463232	193518	269714
Cusp forms	449153	191254	257899
Eisenstein series	14079	2264	11815

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(4140))$

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
4140.2.a	$\chi_{4140}(1, \cdot)$	4140.2.a.a	1	1
		4140.2.a.b	1
		4140.2.a.c	1
		4140.2.a.d	1
		4140.2.a.e	1
		4140.2.a.f	1
		4140.2.a.g	1
		4140.2.a.h	1
		4140.2.a.i	1
		4140.2.a.j	1
		4140.2.a.k	1
		4140.2.a.l	2
		4140.2.a.m	2
		4140.2.a.n	2
		4140.2.a.o	2
		4140.2.a.p	2
		4140.2.a.q	2
		4140.2.a.r	2
		4140.2.a.s	3
		4140.2.a.t	5
		4140.2.a.u	5
4140.2.f	$\chi_{4140}(829, \cdot)$	4140.2.f.a	6	1
		4140.2.f.b	12
		4140.2.f.c	14
		4140.2.f.d	24
4140.2.g	$\chi_{4140}(919, \cdot)$	n/a	356	1
4140.2.h	$\chi_{4140}(1151, \cdot)$	n/a	176	1
4140.2.i	$\chi_{4140}(1241, \cdot)$	4140.2.i.a	16	1
		4140.2.i.b	16
4140.2.n	$\chi_{4140}(2069, \cdot)$	4140.2.n.a	16	1
		4140.2.n.b	32
4140.2.o	$\chi_{4140}(1979, \cdot)$	n/a	264	1
4140.2.p	$\chi_{4140}(91, \cdot)$	n/a	240	1
4140.2.q	$\chi_{4140}(1381, \cdot)$	n/a	176	2
4140.2.r	$\chi_{4140}(827, \cdot)$	n/a	576	2
4140.2.s	$\chi_{4140}(737, \cdot)$	4140.2.s.a	44	2
		4140.2.s.b	44
4140.2.t	$\chi_{4140}(1243, \cdot)$	n/a	660	2
4140.2.u	$\chi_{4140}(1333, \cdot)$	n/a	120	2
4140.2.z	$\chi_{4140}(1471, \cdot)$	n/a	1152	2
4140.2.ba	$\chi_{4140}(689, \cdot)$	n/a	288	2
4140.2.bb	$\chi_{4140}(599, \cdot)$	n/a	1584	2
4140.2.bg	$\chi_{4140}(2531, \cdot)$	n/a	1056	2
4140.2.bh	$\chi_{4140}(2621, \cdot)$	n/a	192	2
4140.2.bi	$\chi_{4140}(2209, \cdot)$	n/a	264	2
4140.2.bj	$\chi_{4140}(2299, \cdot)$	n/a	1712	2
4140.2.bo	$\chi_{4140}(361, \cdot)$	n/a	400	10
4140.2.bt	$\chi_{4140}(1013, \cdot)$	n/a	528	4
4140.2.bu	$\chi_{4140}(1103, \cdot)$	n/a	3424	4
4140.2.bv	$\chi_{4140}(1057, \cdot)$	n/a	576	4
4140.2.bw	$\chi_{4140}(967, \cdot)$	n/a	3168	4
4140.2.bx	$\chi_{4140}(451, \cdot)$	n/a	2400	10
4140.2.by	$\chi_{4140}(179, \cdot)$	n/a	2880	10
4140.2.bz	$\chi_{4140}(89, \cdot)$	n/a	480	10
4140.2.ce	$\chi_{4140}(341, \cdot)$	n/a	320	10
4140.2.cf	$\chi_{4140}(71, \cdot)$	n/a	1920	10
4140.2.cg	$\chi_{4140}(19, \cdot)$	n/a	3560	10
4140.2.ch	$\chi_{4140}(289, \cdot)$	n/a	600	10
4140.2.cm	$\chi_{4140}(121, \cdot)$	n/a	1920	20
4140.2.cr	$\chi_{4140}(37, \cdot)$	n/a	1200	20
4140.2.cs	$\chi_{4140}(127, \cdot)$	n/a	7120	20
4140.2.ct	$\chi_{4140}(197, \cdot)$	n/a	960	20
4140.2.cu	$\chi_{4140}(107, \cdot)$	n/a	5760	20
4140.2.cz	$\chi_{4140}(79, \cdot)$	n/a	17120	20
4140.2.da	$\chi_{4140}(49, \cdot)$	n/a	2880	20
4140.2.db	$\chi_{4140}(221, \cdot)$	n/a	1920	20
4140.2.dc	$\chi_{4140}(131, \cdot)$	n/a	11520	20
4140.2.dh	$\chi_{4140}(59, \cdot)$	n/a	17120	20
4140.2.di	$\chi_{4140}(149, \cdot)$	n/a	2880	20
4140.2.dj	$\chi_{4140}(511, \cdot)$	n/a	11520	20
4140.2.dk	$\chi_{4140}(187, \cdot)$	n/a	34240	40
4140.2.dl	$\chi_{4140}(97, \cdot)$	n/a	5760	40
4140.2.dm	$\chi_{4140}(83, \cdot)$	n/a	34240	40
4140.2.dn	$\chi_{4140}(77, \cdot)$	n/a	5760	40

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(4140))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(4140)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 36}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 16}$$\oplus$$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(12))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(207))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(276))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(414))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(460))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(690))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(828))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1035))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1380))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2070))$$^{\oplus 2}$