Space of modular forms of level 8030 and weight 2

• Label: 8030.2
• Level: 8030
• Weight: 2
• Dimension: 576089
• Nonzero newspaces: 84
• Sturm bound: 7672320

Defining parameters

Level:	\( N \)	=	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 84 \)
Sturm bound:			\(7672320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8030))\).

	Total	New	Old
Modular forms	1929600	576089	1353511
Cusp forms	1906561	576089	1330472
Eisenstein series	23039	0	23039

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8030))\)

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
8030.2.a	\(\chi_{8030}(1, \cdot)\)	8030.2.a.a	1	1
		8030.2.a.b	1
		8030.2.a.c	1
		8030.2.a.d	1
		8030.2.a.e	1
		8030.2.a.f	1
		8030.2.a.g	1
		8030.2.a.h	1
		8030.2.a.i	1
		8030.2.a.j	1
		8030.2.a.k	2
		8030.2.a.l	2
		8030.2.a.m	2
		8030.2.a.n	2
		8030.2.a.o	2
		8030.2.a.p	2
		8030.2.a.q	2
		8030.2.a.r	3
		8030.2.a.s	3
		8030.2.a.t	3
		8030.2.a.u	4
		8030.2.a.v	5
		8030.2.a.w	6
		8030.2.a.x	6
		8030.2.a.y	6
		8030.2.a.z	7
		8030.2.a.ba	7
		8030.2.a.bb	8
		8030.2.a.bc	11
		8030.2.a.bd	14
		8030.2.a.be	15
		8030.2.a.bf	15
		8030.2.a.bg	15
		8030.2.a.bh	17
		8030.2.a.bi	17
		8030.2.a.bj	18
		8030.2.a.bk	18
		8030.2.a.bl	19
8030.2.c	\(\chi_{8030}(4819, \cdot)\)	n/a	360	1
8030.2.e	\(\chi_{8030}(4379, \cdot)\)	n/a	372	1
8030.2.g	\(\chi_{8030}(7591, \cdot)\)	n/a	252	1
8030.2.i	\(\chi_{8030}(1541, \cdot)\)	n/a	504	2
8030.2.j	\(\chi_{8030}(1871, \cdot)\)	n/a	504	2
8030.2.l	\(\chi_{8030}(4553, \cdot)\)	n/a	888	2
8030.2.p	\(\chi_{8030}(5257, \cdot)\)	n/a	864	2
8030.2.q	\(\chi_{8030}(4817, \cdot)\)	n/a	888	2
8030.2.r	\(\chi_{8030}(703, \cdot)\)	n/a	888	2
8030.2.t	\(\chi_{8030}(2509, \cdot)\)	n/a	736	2
8030.2.v	\(\chi_{8030}(731, \cdot)\)	n/a	1152	4
8030.2.w	\(\chi_{8030}(2619, \cdot)\)	n/a	744	2
8030.2.y	\(\chi_{8030}(2839, \cdot)\)	n/a	744	2
8030.2.ba	\(\chi_{8030}(1761, \cdot)\)	n/a	504	2
8030.2.bd	\(\chi_{8030}(3587, \cdot)\)	n/a	1480	4
8030.2.bg	\(\chi_{8030}(2419, \cdot)\)	n/a	1776	4
8030.2.bi	\(\chi_{8030}(241, \cdot)\)	n/a	1184	4
8030.2.bj	\(\chi_{8030}(793, \cdot)\)	n/a	1480	4
8030.2.bl	\(\chi_{8030}(221, \cdot)\)	n/a	1464	6
8030.2.bn	\(\chi_{8030}(291, \cdot)\)	n/a	1184	4
8030.2.bp	\(\chi_{8030}(729, \cdot)\)	n/a	1776	4
8030.2.br	\(\chi_{8030}(1169, \cdot)\)	n/a	1728	4
8030.2.bu	\(\chi_{8030}(441, \cdot)\)	n/a	1008	4
8030.2.bw	\(\chi_{8030}(1363, \cdot)\)	n/a	1776	4
8030.2.bx	\(\chi_{8030}(373, \cdot)\)	n/a	1776	4
8030.2.by	\(\chi_{8030}(593, \cdot)\)	n/a	1776	4
8030.2.cc	\(\chi_{8030}(3893, \cdot)\)	n/a	1776	4
8030.2.ce	\(\chi_{8030}(1849, \cdot)\)	n/a	1472	4
8030.2.cf	\(\chi_{8030}(81, \cdot)\)	n/a	2368	8
8030.2.ci	\(\chi_{8030}(771, \cdot)\)	n/a	1464	6
8030.2.cj	\(\chi_{8030}(529, \cdot)\)	n/a	2232	6
8030.2.cm	\(\chi_{8030}(89, \cdot)\)	n/a	2232	6
8030.2.co	\(\chi_{8030}(119, \cdot)\)	n/a	3552	8
8030.2.cq	\(\chi_{8030}(1487, \cdot)\)	n/a	3552	8
8030.2.cr	\(\chi_{8030}(293, \cdot)\)	n/a	3456	8
8030.2.cs	\(\chi_{8030}(437, \cdot)\)	n/a	3552	8
8030.2.cw	\(\chi_{8030}(173, \cdot)\)	n/a	3552	8
8030.2.cy	\(\chi_{8030}(411, \cdot)\)	n/a	2368	8
8030.2.da	\(\chi_{8030}(1563, \cdot)\)	n/a	2960	8
8030.2.db	\(\chi_{8030}(21, \cdot)\)	n/a	2368	8
8030.2.dd	\(\chi_{8030}(1649, \cdot)\)	n/a	3552	8
8030.2.dg	\(\chi_{8030}(1453, \cdot)\)	n/a	2960	8
8030.2.dj	\(\chi_{8030}(301, \cdot)\)	n/a	2368	8
8030.2.dl	\(\chi_{8030}(9, \cdot)\)	n/a	3552	8
8030.2.dn	\(\chi_{8030}(1159, \cdot)\)	n/a	3552	8
8030.2.dp	\(\chi_{8030}(419, \cdot)\)	n/a	4416	12
8030.2.dr	\(\chi_{8030}(857, \cdot)\)	n/a	5328	12
8030.2.ds	\(\chi_{8030}(967, \cdot)\)	n/a	5328	12
8030.2.du	\(\chi_{8030}(527, \cdot)\)	n/a	5328	12
8030.2.dw	\(\chi_{8030}(1187, \cdot)\)	n/a	5328	12
8030.2.dz	\(\chi_{8030}(111, \cdot)\)	n/a	2928	12
8030.2.eb	\(\chi_{8030}(927, \cdot)\)	n/a	7104	16
8030.2.ec	\(\chi_{8030}(51, \cdot)\)	n/a	4736	16
8030.2.ee	\(\chi_{8030}(679, \cdot)\)	n/a	7104	16
8030.2.eh	\(\chi_{8030}(533, \cdot)\)	n/a	7104	16
8030.2.ei	\(\chi_{8030}(201, \cdot)\)	n/a	7104	24
8030.2.ej	\(\chi_{8030}(49, \cdot)\)	n/a	7104	16
8030.2.el	\(\chi_{8030}(733, \cdot)\)	n/a	7104	16
8030.2.ep	\(\chi_{8030}(227, \cdot)\)	n/a	7104	16
8030.2.eq	\(\chi_{8030}(447, \cdot)\)	n/a	7104	16
8030.2.er	\(\chi_{8030}(633, \cdot)\)	n/a	7104	16
8030.2.et	\(\chi_{8030}(581, \cdot)\)	n/a	4736	16
8030.2.ev	\(\chi_{8030}(177, \cdot)\)	n/a	8880	24
8030.2.ex	\(\chi_{8030}(131, \cdot)\)	n/a	7104	24
8030.2.ez	\(\chi_{8030}(769, \cdot)\)	n/a	10656	24
8030.2.fc	\(\chi_{8030}(133, \cdot)\)	n/a	8880	24
8030.2.fd	\(\chi_{8030}(819, \cdot)\)	n/a	10656	24
8030.2.fg	\(\chi_{8030}(69, \cdot)\)	n/a	10656	24
8030.2.fh	\(\chi_{8030}(71, \cdot)\)	n/a	7104	24
8030.2.fk	\(\chi_{8030}(163, \cdot)\)	n/a	14208	32
8030.2.fn	\(\chi_{8030}(129, \cdot)\)	n/a	14208	32
8030.2.fp	\(\chi_{8030}(271, \cdot)\)	n/a	9472	32
8030.2.fq	\(\chi_{8030}(103, \cdot)\)	n/a	14208	32
8030.2.fs	\(\chi_{8030}(181, \cdot)\)	n/a	14208	48
8030.2.fv	\(\chi_{8030}(123, \cdot)\)	n/a	21312	48
8030.2.fx	\(\chi_{8030}(57, \cdot)\)	n/a	21312	48
8030.2.fz	\(\chi_{8030}(183, \cdot)\)	n/a	21312	48
8030.2.ga	\(\chi_{8030}(127, \cdot)\)	n/a	21312	48
8030.2.gc	\(\chi_{8030}(169, \cdot)\)	n/a	21312	48
8030.2.ge	\(\chi_{8030}(247, \cdot)\)	n/a	42624	96
8030.2.gh	\(\chi_{8030}(29, \cdot)\)	n/a	42624	96
8030.2.gj	\(\chi_{8030}(101, \cdot)\)	n/a	28416	96
8030.2.gl	\(\chi_{8030}(47, \cdot)\)	n/a	42624	96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8030))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8030)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(73))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(146))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(365))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(730))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(803))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1606))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4015))\)\(^{\oplus 2}\)