Space of modular forms of level 4028 and weight 2

• Label: 4028.2
• Level: 4028
• Weight: 2
• Dimension: 291260
• Nonzero newspaces: 36
• Sturm bound: 2021760

Defining parameters

Level:	\( N \)	=	\( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(2021760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4028))\).

	Total	New	Old
Modular forms	510120	294724	215396
Cusp forms	500761	291260	209501
Eisenstein series	9359	3464	5895

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4028))\)

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
4028.2.a	\(\chi_{4028}(1, \cdot)\)	4028.2.a.a	1	1
		4028.2.a.b	1
		4028.2.a.c	19
		4028.2.a.d	19
		4028.2.a.e	19
		4028.2.a.f	19
4028.2.b	\(\chi_{4028}(4027, \cdot)\)	n/a	536	1
4028.2.c	\(\chi_{4028}(3497, \cdot)\)	4028.2.c.a	82	1
4028.2.h	\(\chi_{4028}(531, \cdot)\)	n/a	520	1
4028.2.i	\(\chi_{4028}(425, \cdot)\)	n/a	176	2
4028.2.j	\(\chi_{4028}(189, \cdot)\)	n/a	180	2
4028.2.m	\(\chi_{4028}(3687, \cdot)\)	n/a	972	2
4028.2.n	\(\chi_{4028}(107, \cdot)\)	n/a	1040	2
4028.2.s	\(\chi_{4028}(635, \cdot)\)	n/a	1072	2
4028.2.t	\(\chi_{4028}(2861, \cdot)\)	n/a	180	2
4028.2.u	\(\chi_{4028}(213, \cdot)\)	n/a	516	6
4028.2.w	\(\chi_{4028}(825, \cdot)\)	n/a	360	4
4028.2.x	\(\chi_{4028}(83, \cdot)\)	n/a	2144	4
4028.2.z	\(\chi_{4028}(77, \cdot)\)	n/a	960	12
4028.2.bc	\(\chi_{4028}(529, \cdot)\)	n/a	540	6
4028.2.bd	\(\chi_{4028}(319, \cdot)\)	n/a	3120	6
4028.2.bf	\(\chi_{4028}(211, \cdot)\)	n/a	3216	6
4028.2.bh	\(\chi_{4028}(227, \cdot)\)	n/a	6432	12
4028.2.bm	\(\chi_{4028}(229, \cdot)\)	n/a	984	12
4028.2.bn	\(\chi_{4028}(303, \cdot)\)	n/a	6432	12
4028.2.bo	\(\chi_{4028}(23, \cdot)\)	n/a	6432	12
4028.2.br	\(\chi_{4028}(129, \cdot)\)	n/a	1080	12
4028.2.bs	\(\chi_{4028}(49, \cdot)\)	n/a	2160	24
4028.2.bt	\(\chi_{4028}(39, \cdot)\)	n/a	11664	24
4028.2.bw	\(\chi_{4028}(569, \cdot)\)	n/a	2160	24
4028.2.bx	\(\chi_{4028}(197, \cdot)\)	n/a	2160	24
4028.2.by	\(\chi_{4028}(255, \cdot)\)	n/a	12864	24
4028.2.cd	\(\chi_{4028}(183, \cdot)\)	n/a	12864	24
4028.2.ce	\(\chi_{4028}(81, \cdot)\)	n/a	6480	72
4028.2.cg	\(\chi_{4028}(87, \cdot)\)	n/a	25728	48
4028.2.ch	\(\chi_{4028}(65, \cdot)\)	n/a	4320	48
4028.2.ck	\(\chi_{4028}(59, \cdot)\)	n/a	38592	72
4028.2.cm	\(\chi_{4028}(15, \cdot)\)	n/a	38592	72
4028.2.cn	\(\chi_{4028}(9, \cdot)\)	n/a	6480	72
4028.2.cq	\(\chi_{4028}(21, \cdot)\)	n/a	12960	144
4028.2.ct	\(\chi_{4028}(35, \cdot)\)	n/a	77184	144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(212))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1007))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2014))\)\(^{\oplus 2}\)