Space of modular forms of level 4332 and weight 2

• Label: 4332.2
• Level: 4332
• Weight: 2
• Dimension: 225234
• Nonzero newspaces: 24
• Sturm bound: 2079360

Defining parameters

Level:	\( N \)	=	\( 4332 = 2^{2} \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(2079360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4332))\).

	Total	New	Old
Modular forms	524880	227110	297770
Cusp forms	514801	225234	289567
Eisenstein series	10079	1876	8203

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4332))\)

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
4332.2.a	\(\chi_{4332}(1, \cdot)\)	4332.2.a.a	1	1
		4332.2.a.b	1
		4332.2.a.c	1
		4332.2.a.d	1
		4332.2.a.e	2
		4332.2.a.f	2
		4332.2.a.g	2
		4332.2.a.h	2
		4332.2.a.i	2
		4332.2.a.j	2
		4332.2.a.k	2
		4332.2.a.l	2
		4332.2.a.m	2
		4332.2.a.n	3
		4332.2.a.o	3
		4332.2.a.p	4
		4332.2.a.q	4
		4332.2.a.r	4
		4332.2.a.s	4
		4332.2.a.t	6
		4332.2.a.u	6
4332.2.c	\(\chi_{4332}(3611, \cdot)\)	n/a	648	1
4332.2.d	\(\chi_{4332}(2165, \cdot)\)	n/a	114	1
4332.2.f	\(\chi_{4332}(2887, \cdot)\)	n/a	340	1
4332.2.i	\(\chi_{4332}(1873, \cdot)\)	n/a	112	2
4332.2.k	\(\chi_{4332}(1015, \cdot)\)	n/a	680	2
4332.2.m	\(\chi_{4332}(1151, \cdot)\)	n/a	1296	2
4332.2.p	\(\chi_{4332}(293, \cdot)\)	n/a	228	2
4332.2.q	\(\chi_{4332}(2581, \cdot)\)	n/a	342	6
4332.2.t	\(\chi_{4332}(2465, \cdot)\)	n/a	678	6
4332.2.v	\(\chi_{4332}(1859, \cdot)\)	n/a	3888	6
4332.2.w	\(\chi_{4332}(127, \cdot)\)	n/a	2040	6
4332.2.y	\(\chi_{4332}(229, \cdot)\)	n/a	1152	18
4332.2.bb	\(\chi_{4332}(151, \cdot)\)	n/a	6840	18
4332.2.bd	\(\chi_{4332}(113, \cdot)\)	n/a	2268	18
4332.2.be	\(\chi_{4332}(191, \cdot)\)	n/a	13608	18
4332.2.bg	\(\chi_{4332}(49, \cdot)\)	n/a	2304	36
4332.2.bh	\(\chi_{4332}(65, \cdot)\)	n/a	4536	36
4332.2.bk	\(\chi_{4332}(11, \cdot)\)	n/a	27216	36
4332.2.bm	\(\chi_{4332}(31, \cdot)\)	n/a	13680	36
4332.2.bo	\(\chi_{4332}(25, \cdot)\)	n/a	6804	108
4332.2.bq	\(\chi_{4332}(67, \cdot)\)	n/a	41040	108
4332.2.br	\(\chi_{4332}(23, \cdot)\)	n/a	81648	108
4332.2.bt	\(\chi_{4332}(29, \cdot)\)	n/a	13716	108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4332))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4332)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2166))\)\(^{\oplus 2}\)