Space of modular forms of level 498, weight 2, and Character 498.f

• Label: 498.2.f
• Level: $498$
• Weight: $2$
• Character orbit: 498.f
• Rep. character: $\chi_{498}(5,\cdot)$
• Character field: $\Q(\zeta_{82})$
• Dimension: $1120$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 498 = 2 \cdot 3 \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	498.f (of order \(82\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 249 \)
Character field:			\(\Q(\zeta_{82})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(498, [\chi])\).

	Total	New	Old
Modular forms	3520	1120	2400
Cusp forms	3200	1120	2080
Eisenstein series	320	0	320

Trace form

\( 1120 q + 2 q^{3} - 28 q^{4} + 4 q^{7} - 14 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(498, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
498.2.f.a	$498$	$2$	498.f	249.f	$82$	$560$	$14$	$3.977$		None		✓	498.2.f.a	$2$	$0$	\(-14\)	\(1\)	\(2\)	\(2\)		$\mathrm{SU}(2)[C_{82}]$
498.2.f.b	$498$	$2$	498.f	249.f	$82$	$560$	$14$	$3.977$		None		✓	498.2.f.a	$2$	$0$	\(14\)	\(1\)	\(-2\)	\(2\)		$\mathrm{SU}(2)[C_{82}]$

Decomposition of \(S_{2}^{\mathrm{old}}(498, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(498, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(249, [\chi])\)\(^{\oplus 2}\)