Space of modular forms of level 4304 and weight 2

• Label: 4304.2
• Level: 4304
• Weight: 2
• Dimension: 324410
• Nonzero newspaces: 14
• Sturm bound: 2315520

Defining parameters

Level:	\( N \)	=	\( 4304 = 2^{4} \cdot 269 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 14 \)
Sturm bound:			\(2315520\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4304))\).

	Total	New	Old
Modular forms	582632	326812	255820
Cusp forms	575129	324410	250719
Eisenstein series	7503	2402	5101

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4304))\)

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
4304.2.a	\(\chi_{4304}(1, \cdot)\)	4304.2.a.a	1	1
		4304.2.a.b	1
		4304.2.a.c	2
		4304.2.a.d	2
		4304.2.a.e	4
		4304.2.a.f	5
		4304.2.a.g	6
		4304.2.a.h	7
		4304.2.a.i	7
		4304.2.a.j	13
		4304.2.a.k	15
		4304.2.a.l	16
		4304.2.a.m	17
		4304.2.a.n	18
		4304.2.a.o	20
4304.2.b	\(\chi_{4304}(2153, \cdot)\)	None	0	1
4304.2.e	\(\chi_{4304}(2689, \cdot)\)	n/a	134	1
4304.2.f	\(\chi_{4304}(537, \cdot)\)	None	0	1
4304.2.j	\(\chi_{4304}(187, \cdot)\)	n/a	1076	2
4304.2.k	\(\chi_{4304}(2503, \cdot)\)	None	0	2
4304.2.n	\(\chi_{4304}(1077, \cdot)\)	n/a	1072	2
4304.2.o	\(\chi_{4304}(1613, \cdot)\)	n/a	1076	2
4304.2.r	\(\chi_{4304}(351, \cdot)\)	n/a	270	2
4304.2.t	\(\chi_{4304}(2339, \cdot)\)	n/a	1076	2
4304.2.u	\(\chi_{4304}(81, \cdot)\)	n/a	8844	66
4304.2.x	\(\chi_{4304}(9, \cdot)\)	None	0	66
4304.2.y	\(\chi_{4304}(49, \cdot)\)	n/a	8844	66
4304.2.bb	\(\chi_{4304}(25, \cdot)\)	None	0	66
4304.2.bc	\(\chi_{4304}(19, \cdot)\)	n/a	71016	132
4304.2.be	\(\chi_{4304}(15, \cdot)\)	n/a	17820	132
4304.2.bh	\(\chi_{4304}(13, \cdot)\)	n/a	71016	132
4304.2.bi	\(\chi_{4304}(5, \cdot)\)	n/a	71016	132
4304.2.bl	\(\chi_{4304}(7, \cdot)\)	None	0	132
4304.2.bm	\(\chi_{4304}(3, \cdot)\)	n/a	71016	132

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4304))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4304)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(269))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(538))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1076))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4304))\)\(^{\oplus 1}\)