Space of modular forms of level 598 and weight 2

• Label: 598.2
• Level: 598
• Weight: 2
• Dimension: 3641
• Nonzero newspaces: 12
• Newform subspaces: 34
• Sturm bound: 44352
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 598 = 2 \cdot 13 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 34 \)
Sturm bound:			\(44352\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(598))\).

	Total	New	Old
Modular forms	11616	3641	7975
Cusp forms	10561	3641	6920
Eisenstein series	1055	0	1055

Trace form

3641 * q + 3 * q^2 + 12 * q^3 + 3 * q^4 + 18 * q^5 + 12 * q^6 + 16 * q^7 - 3 * q^8 + 7 * q^9 - 12 * q^10 + 12 * q^11 + 4 * q^12 - 21 * q^13 - 20 * q^15 - 5 * q^16 - 20 * q^17 - 79 * q^18 - 40 * q^19 - 32 * q^20 - 92 * q^21 - 8 * q^22 - 53 * q^23 + 12 * q^24 - 25 * q^25 + 5 * q^26 - 84 * q^27 - 28 * q^28 - 32 * q^29 - 64 * q^30 - 28 * q^31 + 3 * q^32 - 20 * q^33 + 6 * q^34 - 44 * q^35 - 9 * q^36 - 36 * q^37 - 12 * q^38 - 40 * q^39 + 18 * q^40 - 20 * q^41 + 24 * q^42 - 44 * q^43 - 12 * q^44 - 48 * q^45 + 23 * q^46 - 40 * q^47 + 12 * q^48 - 25 * q^49 + 39 * q^50 - 16 * q^51 + 13 * q^52 + 46 * q^53 + 4 * q^54 - 80 * q^55 - 44 * q^56 - 108 * q^57 - 52 * q^58 - 136 * q^59 - 20 * q^60 - 68 * q^61 - 108 * q^62 - 156 * q^63 - 3 * q^64 - 166 * q^65 - 128 * q^66 - 36 * q^67 - 40 * q^68 - 152 * q^69 - 104 * q^70 - 148 * q^71 - 97 * q^72 - 42 * q^73 - 140 * q^74 - 276 * q^75 + 4 * q^76 - 172 * q^77 - 78 * q^78 - 172 * q^79 - 32 * q^80 - 149 * q^81 - 64 * q^82 - 116 * q^83 - 4 * q^84 - 54 * q^85 + 40 * q^86 - 12 * q^87 + 36 * q^88 + 34 * q^89 + 114 * q^90 + 20 * q^91 + 23 * q^92 + 160 * q^93 + 24 * q^94 + 84 * q^95 + 12 * q^96 - 82 * q^97 - 13 * q^98 - 100 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(598))\)

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
598.2.a	\(\chi_{598}(1, \cdot)\)	598.2.a.a	1	1
		598.2.a.b	1
		598.2.a.c	1
		598.2.a.d	1
		598.2.a.e	2
		598.2.a.f	2
		598.2.a.g	2
		598.2.a.h	2
		598.2.a.i	4
		598.2.a.j	5
598.2.c	\(\chi_{598}(415, \cdot)\)	598.2.c.a	6	1
		598.2.c.b	6
		598.2.c.c	12
598.2.e	\(\chi_{598}(139, \cdot)\)	598.2.e.a	12	2
		598.2.e.b	12
		598.2.e.c	14
		598.2.e.d	14
598.2.g	\(\chi_{598}(229, \cdot)\)	598.2.g.a	56	2
598.2.h	\(\chi_{598}(231, \cdot)\)	598.2.h.a	4	2
		598.2.h.b	24
		598.2.h.c	28
598.2.k	\(\chi_{598}(27, \cdot)\)	598.2.k.a	10	10
		598.2.k.b	10
		598.2.k.c	40
		598.2.k.d	60
		598.2.k.e	60
		598.2.k.f	60
598.2.l	\(\chi_{598}(45, \cdot)\)	598.2.l.a	112	4
598.2.o	\(\chi_{598}(25, \cdot)\)	598.2.o.a	280	10
598.2.q	\(\chi_{598}(3, \cdot)\)	598.2.q.a	280	20
		598.2.q.b	280
598.2.r	\(\chi_{598}(5, \cdot)\)	598.2.r.a	560	20
598.2.v	\(\chi_{598}(49, \cdot)\)	598.2.v.a	560	20
598.2.x	\(\chi_{598}(7, \cdot)\)	598.2.x.a	1120	40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(598))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(598)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(299))\)\(^{\oplus 2}\)