Space of modular forms of level 15800 and weight 2

• Label: 15800.2
• Level: 15800
• Weight: 2
• Dimension: 3874502
• Nonzero newspaces: 72
• Sturm bound: 29952000

Defining parameters

Level:	$N$	=	$15800 = 2^{3} \cdot 5^{2} \cdot 79$
Weight:	$k$	=	$2$
Nonzero newspaces:			$72$
Sturm bound:			$29952000$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(15800))$.

	Total	New	Old
Modular forms	7514208	3887130	3627078
Cusp forms	7461793	3874502	3587291
Eisenstein series	52415	12628	39787

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(15800))$

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
15800.2.a	$\chi_{15800}(1, \cdot)$	15800.2.a.a	1	1
		15800.2.a.b	1
		15800.2.a.c	1
		15800.2.a.d	1
		15800.2.a.e	1
		15800.2.a.f	2
		15800.2.a.g	2
		15800.2.a.h	2
		15800.2.a.i	3
		15800.2.a.j	4
		15800.2.a.k	5
		15800.2.a.l	6
		15800.2.a.m	6
		15800.2.a.n	7
		15800.2.a.o	7
		15800.2.a.p	8
		15800.2.a.q	13
		15800.2.a.r	13
		15800.2.a.s	15
		15800.2.a.t	17
		15800.2.a.u	17
		15800.2.a.v	18
		15800.2.a.w	18
		15800.2.a.x	21
		15800.2.a.y	21
		15800.2.a.z	22
		15800.2.a.ba	22
		15800.2.a.bb	29
		15800.2.a.bc	29
		15800.2.a.bd	29
		15800.2.a.be	29
15800.2.d	$\chi_{15800}(8849, \cdot)$	n/a	352	1
15800.2.f	$\chi_{15800}(7901, \cdot)$	n/a	1482	1
15800.2.h	$\chi_{15800}(14851, \cdot)$	n/a	1514	1
15800.2.k	$\chi_{15800}(949, \cdot)$	n/a	1404	1
15800.2.m	$\chi_{15800}(7899, \cdot)$	n/a	1436	1
15800.2.q	$\chi_{15800}(13801, \cdot)$	n/a	760	2
15800.2.r	$\chi_{15800}(157, \cdot)$	n/a	2872	2
15800.2.w	$\chi_{15800}(1107, \cdot)$	n/a	2808	2
15800.2.y	$\chi_{15800}(6793, \cdot)$	n/a	720	2
15800.2.z	$\chi_{15800}(3161, \cdot)$	n/a	2344	4
15800.2.bd	$\chi_{15800}(9299, \cdot)$	n/a	2872	2
15800.2.bf	$\chi_{15800}(14749, \cdot)$	n/a	2872	2
15800.2.bi	$\chi_{15800}(451, \cdot)$	n/a	3028	2
15800.2.bk	$\chi_{15800}(5901, \cdot)$	n/a	3028	2
15800.2.bm	$\chi_{15800}(6849, \cdot)$	n/a	720	2
15800.2.bp	$\chi_{15800}(1579, \cdot)$	n/a	9584	4
15800.2.br	$\chi_{15800}(4109, \cdot)$	n/a	9360	4
15800.2.bx	$\chi_{15800}(2529, \cdot)$	n/a	2336	4
15800.2.cb	$\chi_{15800}(2211, \cdot)$	n/a	9584	4
15800.2.cd	$\chi_{15800}(1581, \cdot)$	n/a	9360	4
15800.2.ce	$\chi_{15800}(13643, \cdot)$	n/a	5744	4
15800.2.cg	$\chi_{15800}(8193, \cdot)$	n/a	1440	4
15800.2.cj	$\chi_{15800}(293, \cdot)$	n/a	5744	4
15800.2.cm	$\chi_{15800}(1601, \cdot)$	n/a	4560	12
15800.2.cn	$\chi_{15800}(1161, \cdot)$	n/a	4800	8
15800.2.co	$\chi_{15800}(473, \cdot)$	n/a	4800	8
15800.2.cq	$\chi_{15800}(3003, \cdot)$	n/a	18720	8
15800.2.cv	$\chi_{15800}(2053, \cdot)$	n/a	19168	8
15800.2.cz	$\chi_{15800}(4299, \cdot)$	n/a	17232	12
15800.2.db	$\chi_{15800}(749, \cdot)$	n/a	17232	12
15800.2.de	$\chi_{15800}(251, \cdot)$	n/a	18168	12
15800.2.dg	$\chi_{15800}(101, \cdot)$	n/a	18168	12
15800.2.di	$\chi_{15800}(1049, \cdot)$	n/a	4320	12
15800.2.dl	$\chi_{15800}(181, \cdot)$	n/a	19168	8
15800.2.dn	$\chi_{15800}(3611, \cdot)$	n/a	19168	8
15800.2.dr	$\chi_{15800}(529, \cdot)$	n/a	4800	8
15800.2.dx	$\chi_{15800}(2109, \cdot)$	n/a	19168	8
15800.2.dz	$\chi_{15800}(419, \cdot)$	n/a	19168	8
15800.2.ea	$\chi_{15800}(801, \cdot)$	n/a	9120	24
15800.2.eb	$\chi_{15800}(57, \cdot)$	n/a	8640	24
15800.2.ed	$\chi_{15800}(907, \cdot)$	n/a	34464	24
15800.2.ei	$\chi_{15800}(93, \cdot)$	n/a	34464	24
15800.2.el	$\chi_{15800}(3453, \cdot)$	n/a	38336	16
15800.2.eo	$\chi_{15800}(577, \cdot)$	n/a	9600	16
15800.2.eq	$\chi_{15800}(1003, \cdot)$	n/a	38336	16
15800.2.er	$\chi_{15800}(441, \cdot)$	n/a	28800	48
15800.2.eu	$\chi_{15800}(49, \cdot)$	n/a	8640	24
15800.2.ew	$\chi_{15800}(901, \cdot)$	n/a	36336	24
15800.2.ey	$\chi_{15800}(1251, \cdot)$	n/a	36336	24
15800.2.fb	$\chi_{15800}(1749, \cdot)$	n/a	34464	24
15800.2.fd	$\chi_{15800}(899, \cdot)$	n/a	34464	24
15800.2.fh	$\chi_{15800}(21, \cdot)$	n/a	115008	48
15800.2.fj	$\chi_{15800}(91, \cdot)$	n/a	115008	48
15800.2.fn	$\chi_{15800}(89, \cdot)$	n/a	28800	48
15800.2.ft	$\chi_{15800}(1389, \cdot)$	n/a	115008	48
15800.2.fv	$\chi_{15800}(219, \cdot)$	n/a	115008	48
15800.2.fy	$\chi_{15800}(1093, \cdot)$	n/a	68928	48
15800.2.gb	$\chi_{15800}(193, \cdot)$	n/a	17280	48
15800.2.gd	$\chi_{15800}(643, \cdot)$	n/a	68928	48
15800.2.ge	$\chi_{15800}(81, \cdot)$	n/a	57600	96
15800.2.gf	$\chi_{15800}(173, \cdot)$	n/a	230016	96
15800.2.gk	$\chi_{15800}(67, \cdot)$	n/a	230016	96
15800.2.gm	$\chi_{15800}(17, \cdot)$	n/a	57600	96
15800.2.gn	$\chi_{15800}(59, \cdot)$	n/a	230016	96
15800.2.gp	$\chi_{15800}(189, \cdot)$	n/a	230016	96
15800.2.gv	$\chi_{15800}(9, \cdot)$	n/a	57600	96
15800.2.gz	$\chi_{15800}(211, \cdot)$	n/a	230016	96
15800.2.hb	$\chi_{15800}(341, \cdot)$	n/a	230016	96
15800.2.hc	$\chi_{15800}(83, \cdot)$	n/a	460032	192
15800.2.he	$\chi_{15800}(113, \cdot)$	n/a	115200	192
15800.2.hh	$\chi_{15800}(37, \cdot)$	n/a	460032	192

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(15800))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(15800)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(79))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(158))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(316))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(395))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(632))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(790))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1580))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1975))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3160))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3950))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7900))$$^{\oplus 2}$