Space of modular forms of level 4598 and weight 2

• Label: 4598.2
• Level: 4598
• Weight: 2
• Dimension: 213023
• Nonzero newspaces: 24
• Sturm bound: 2613600

Defining parameters

Level:	\( N \)	=	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(2613600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4598))\).

	Total	New	Old
Modular forms	659160	213023	446137
Cusp forms	647641	213023	434618
Eisenstein series	11519	0	11519

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4598))\)

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
4598.2.a	\(\chi_{4598}(1, \cdot)\)	4598.2.a.a	1	1
		4598.2.a.b	1
		4598.2.a.c	1
		4598.2.a.d	1
		4598.2.a.e	1
		4598.2.a.f	1
		4598.2.a.g	1
		4598.2.a.h	1
		4598.2.a.i	1
		4598.2.a.j	1
		4598.2.a.k	1
		4598.2.a.l	1
		4598.2.a.m	1
		4598.2.a.n	1
		4598.2.a.o	1
		4598.2.a.p	1
		4598.2.a.q	1
		4598.2.a.r	1
		4598.2.a.s	1
		4598.2.a.t	2
		4598.2.a.u	2
		4598.2.a.v	2
		4598.2.a.w	2
		4598.2.a.x	2
		4598.2.a.y	2
		4598.2.a.z	2
		4598.2.a.ba	2
		4598.2.a.bb	2
		4598.2.a.bc	2
		4598.2.a.bd	2
		4598.2.a.be	2
		4598.2.a.bf	2
		4598.2.a.bg	2
		4598.2.a.bh	2
		4598.2.a.bi	2
		4598.2.a.bj	2
		4598.2.a.bk	3
		4598.2.a.bl	3
		4598.2.a.bm	3
		4598.2.a.bn	3
		4598.2.a.bo	3
		4598.2.a.bp	3
		4598.2.a.bq	4
		4598.2.a.br	4
		4598.2.a.bs	4
		4598.2.a.bt	4
		4598.2.a.bu	4
		4598.2.a.bv	4
		4598.2.a.bw	8
		4598.2.a.bx	8
		4598.2.a.by	8
		4598.2.a.bz	8
		4598.2.a.ca	8
		4598.2.a.cb	8
		4598.2.a.cc	10
		4598.2.a.cd	10
4598.2.b	\(\chi_{4598}(4597, \cdot)\)	n/a	180	1
4598.2.e	\(\chi_{4598}(3389, \cdot)\)	n/a	366	2
4598.2.f	\(\chi_{4598}(1939, \cdot)\)	n/a	648	4
4598.2.h	\(\chi_{4598}(483, \cdot)\)	n/a	360	2
4598.2.j	\(\chi_{4598}(727, \cdot)\)	n/a	1086	6
4598.2.m	\(\chi_{4598}(645, \cdot)\)	n/a	720	4
4598.2.n	\(\chi_{4598}(419, \cdot)\)	n/a	1980	10
4598.2.o	\(\chi_{4598}(729, \cdot)\)	n/a	1440	8
4598.2.r	\(\chi_{4598}(241, \cdot)\)	n/a	1080	6
4598.2.t	\(\chi_{4598}(417, \cdot)\)	n/a	2200	10
4598.2.w	\(\chi_{4598}(1129, \cdot)\)	n/a	1440	8
4598.2.y	\(\chi_{4598}(45, \cdot)\)	n/a	4400	20
4598.2.z	\(\chi_{4598}(9, \cdot)\)	n/a	4320	24
4598.2.ba	\(\chi_{4598}(115, \cdot)\)	n/a	7920	40
4598.2.bd	\(\chi_{4598}(65, \cdot)\)	n/a	4400	20
4598.2.be	\(\chi_{4598}(699, \cdot)\)	n/a	4320	24
4598.2.bh	\(\chi_{4598}(23, \cdot)\)	n/a	13200	60
4598.2.bj	\(\chi_{4598}(151, \cdot)\)	n/a	8800	40
4598.2.bl	\(\chi_{4598}(49, \cdot)\)	n/a	17600	80
4598.2.bn	\(\chi_{4598}(21, \cdot)\)	n/a	13200	60
4598.2.bp	\(\chi_{4598}(107, \cdot)\)	n/a	17600	80
4598.2.bs	\(\chi_{4598}(5, \cdot)\)	n/a	52800	240
4598.2.bu	\(\chi_{4598}(13, \cdot)\)	n/a	52800	240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4598))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4598)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(418))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2299))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4598))\)\(^{\oplus 1}\)