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 + 4 * q^10 + 2 * q^12 - 28 * q^16 + 22 * q^21 - 32 * q^25 + 20 * q^27 + 4 * q^28 + 4 * q^30 - 4 * q^31 + 18 * q^33 - 14 * q^36 + 4 * q^40 + 2 * q^48 - 24 * q^49 + 18 * q^51 + 16 * q^61 + 14 * q^63 - 28 * q^64 - 41 * q^66 - 234 * q^69 + 8 * q^70 - 564 * q^75 - 402 * q^78 - 318 * q^81 - 224 * q^84 - 322 * q^87 - 414 * q^90 - 548 * q^93 + 24 * q^94 - 216 * q^99

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	Largest	Maximal	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}$