Space of modular forms of level 9036 and weight 2

• Label: 9036.2
• Level: 9036
• Weight: 2
• Dimension: 1045099
• Nonzero newspaces: 32
• Sturm bound: 9072000

Defining parameters

Level:	\( N \)	=	\( 9036 = 2^{2} \cdot 3^{2} \cdot 251 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(9072000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9036))\).

	Total	New	Old
Modular forms	2278000	1049583	1228417
Cusp forms	2258001	1045099	1212902
Eisenstein series	19999	4484	15515

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9036))\)

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
9036.2.a	\(\chi_{9036}(1, \cdot)\)	9036.2.a.a	1	1
		9036.2.a.b	1
		9036.2.a.c	1
		9036.2.a.d	1
		9036.2.a.e	1
		9036.2.a.f	1
		9036.2.a.g	1
		9036.2.a.h	6
		9036.2.a.i	7
		9036.2.a.j	9
		9036.2.a.k	10
		9036.2.a.l	12
		9036.2.a.m	14
		9036.2.a.n	19
		9036.2.a.o	19
9036.2.c	\(\chi_{9036}(503, \cdot)\)	n/a	500	1
9036.2.e	\(\chi_{9036}(4517, \cdot)\)	9036.2.e.a	84	1
9036.2.g	\(\chi_{9036}(4015, \cdot)\)	n/a	628	1
9036.2.i	\(\chi_{9036}(3013, \cdot)\)	n/a	500	2
9036.2.j	\(\chi_{9036}(721, \cdot)\)	n/a	420	4
9036.2.l	\(\chi_{9036}(1003, \cdot)\)	n/a	3016	2
9036.2.n	\(\chi_{9036}(1505, \cdot)\)	n/a	504	2
9036.2.p	\(\chi_{9036}(3515, \cdot)\)	n/a	3000	2
9036.2.r	\(\chi_{9036}(3365, \cdot)\)	n/a	336	4
9036.2.t	\(\chi_{9036}(1223, \cdot)\)	n/a	2016	4
9036.2.w	\(\chi_{9036}(2863, \cdot)\)	n/a	2512	4
9036.2.y	\(\chi_{9036}(1777, \cdot)\)	n/a	2016	8
9036.2.z	\(\chi_{9036}(757, \cdot)\)	n/a	2100	20
9036.2.bb	\(\chi_{9036}(283, \cdot)\)	n/a	12064	8
9036.2.be	\(\chi_{9036}(2279, \cdot)\)	n/a	12064	8
9036.2.bg	\(\chi_{9036}(353, \cdot)\)	n/a	2016	8
9036.2.bh	\(\chi_{9036}(235, \cdot)\)	n/a	12560	20
9036.2.bk	\(\chi_{9036}(377, \cdot)\)	n/a	1680	20
9036.2.bl	\(\chi_{9036}(1259, \cdot)\)	n/a	10080	20
9036.2.bo	\(\chi_{9036}(25, \cdot)\)	n/a	10080	40
9036.2.bp	\(\chi_{9036}(73, \cdot)\)	n/a	10500	100
9036.2.bs	\(\chi_{9036}(497, \cdot)\)	n/a	10080	40
9036.2.bt	\(\chi_{9036}(455, \cdot)\)	n/a	60320	40
9036.2.bw	\(\chi_{9036}(151, \cdot)\)	n/a	60320	40
9036.2.by	\(\chi_{9036}(19, \cdot)\)	n/a	62800	100
9036.2.cb	\(\chi_{9036}(53, \cdot)\)	n/a	8400	100
9036.2.cd	\(\chi_{9036}(35, \cdot)\)	n/a	50400	100
9036.2.ce	\(\chi_{9036}(13, \cdot)\)	n/a	50400	200
9036.2.cf	\(\chi_{9036}(29, \cdot)\)	n/a	50400	200
9036.2.ch	\(\chi_{9036}(23, \cdot)\)	n/a	301600	200
9036.2.cl	\(\chi_{9036}(43, \cdot)\)	n/a	301600	200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9036))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9036)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(502))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(753))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1004))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1506))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2259))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3012))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4518))\)\(^{\oplus 2}\)