Space of modular forms of level 598, weight 2, and Character 598.g

• Label: 598.2.g
• Level: $598$
• Weight: $2$
• Character orbit: 598.g
• Rep. character: $\chi_{598}(229,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 598 = 2 \cdot 13 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	598.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 299 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(598, [\chi])\).

	Total	New	Old
Modular forms	176	56	120
Cusp forms	160	56	104
Eisenstein series	16	0	16

Trace form

56 * q + 56 * q^9 + 8 * q^13 - 56 * q^16 - 8 * q^26 + 48 * q^27 + 16 * q^29 + 32 * q^31 - 32 * q^35 + 16 * q^39 - 32 * q^41 + 12 * q^46 - 48 * q^47 + 16 * q^50 - 48 * q^54 - 64 * q^55 - 8 * q^58 + 48 * q^59 - 24 * q^70 - 32 * q^71 + 8 * q^73 - 16 * q^78 - 8 * q^81 + 80 * q^85 + 128 * q^87 + 32 * q^92 - 72 * q^93 - 80 * q^94 + 16 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(598, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
598.2.g.a	$598$	$2$	598.g	299.g	$4$	$56$	$28$	$4.775$		None		✓	✓	✓	598.2.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(598, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(598, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(299, [\chi])\)\(^{\oplus 2}\)