Space of modular forms of level 5488 and weight 2

• Label: 5488.2
• Level: 5488
• Weight: 2
• Dimension: 495720
• Nonzero newspaces: 24
• Sturm bound: 3687936

Defining parameters

Level:	$N$	=	$5488 = 2^{4} \cdot 7^{3}$
Weight:	$k$	=	$2$
Nonzero newspaces:			$24$
Sturm bound:			$3687936$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(5488))$.

	Total	New	Old
Modular forms	929628	499608	430020
Cusp forms	914341	495720	418621
Eisenstein series	15287	3888	11399

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(5488))$

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
5488.2.a	$\chi_{5488}(1, \cdot)$	5488.2.a.a	3	1
		5488.2.a.b	3
		5488.2.a.c	3
		5488.2.a.d	3
		5488.2.a.e	3
		5488.2.a.f	3
		5488.2.a.g	6
		5488.2.a.h	6
		5488.2.a.i	6
		5488.2.a.j	6
		5488.2.a.k	6
		5488.2.a.l	6
		5488.2.a.m	6
		5488.2.a.n	6
		5488.2.a.o	6
		5488.2.a.p	6
		5488.2.a.q	6
		5488.2.a.r	9
		5488.2.a.s	9
		5488.2.a.t	9
		5488.2.a.u	9
		5488.2.a.v	12
		5488.2.a.w	12
5488.2.b	$\chi_{5488}(2745, \cdot)$	None	0	1
5488.2.e	$\chi_{5488}(2743, \cdot)$	None	0	1
5488.2.f	$\chi_{5488}(5487, \cdot)$	n/a	144	1
5488.2.i	$\chi_{5488}(3105, \cdot)$	n/a	288	2
5488.2.j	$\chi_{5488}(1371, \cdot)$	n/a	1152	2
5488.2.m	$\chi_{5488}(1373, \cdot)$	n/a	1152	2
5488.2.p	$\chi_{5488}(1391, \cdot)$	n/a	288	2
5488.2.q	$\chi_{5488}(4135, \cdot)$	None	0	2
5488.2.t	$\chi_{5488}(361, \cdot)$	None	0	2
5488.2.u	$\chi_{5488}(785, \cdot)$	n/a	810	6
5488.2.w	$\chi_{5488}(19, \cdot)$	n/a	2304	4
5488.2.x	$\chi_{5488}(1733, \cdot)$	n/a	2304	4
5488.2.bb	$\chi_{5488}(783, \cdot)$	n/a	840	6
5488.2.bc	$\chi_{5488}(391, \cdot)$	None	0	6
5488.2.bf	$\chi_{5488}(393, \cdot)$	None	0	6
5488.2.bg	$\chi_{5488}(177, \cdot)$	n/a	1620	12
5488.2.bh	$\chi_{5488}(197, \cdot)$	n/a	6600	12
5488.2.bk	$\chi_{5488}(195, \cdot)$	n/a	6600	12
5488.2.bl	$\chi_{5488}(569, \cdot)$	None	0	12
5488.2.bo	$\chi_{5488}(215, \cdot)$	None	0	12
5488.2.bp	$\chi_{5488}(31, \cdot)$	n/a	1680	12
5488.2.bs	$\chi_{5488}(113, \cdot)$	n/a	8190	42
5488.2.bu	$\chi_{5488}(165, \cdot)$	n/a	13200	24
5488.2.bv	$\chi_{5488}(227, \cdot)$	n/a	13200	24
5488.2.bx	$\chi_{5488}(55, \cdot)$	None	0	42
5488.2.by	$\chi_{5488}(57, \cdot)$	None	0	42
5488.2.cb	$\chi_{5488}(111, \cdot)$	n/a	8232	42
5488.2.ce	$\chi_{5488}(65, \cdot)$	n/a	16380	84
5488.2.cf	$\chi_{5488}(29, \cdot)$	n/a	65688	84
5488.2.cg	$\chi_{5488}(27, \cdot)$	n/a	65688	84
5488.2.cl	$\chi_{5488}(47, \cdot)$	n/a	16464	84
5488.2.co	$\chi_{5488}(9, \cdot)$	None	0	84
5488.2.cp	$\chi_{5488}(87, \cdot)$	None	0	84
5488.2.cs	$\chi_{5488}(3, \cdot)$	n/a	131376	168
5488.2.ct	$\chi_{5488}(37, \cdot)$	n/a	131376	168

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(5488))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(5488)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 15}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(343))$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(686))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(784))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1372))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2744))$$^{\oplus 2}$