Space of modular forms of level 494, weight 2, and Character 494.g

• Label: 494.2.g
• Level: $494$
• Weight: $2$
• Character orbit: 494.g
• Rep. character: $\chi_{494}(191,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $6$
• Sturm bound: $140$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(140\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(494, [\chi])\).

	Total	New	Old
Modular forms	148	40	108
Cusp forms	132	40	92
Eisenstein series	16	0	16

Trace form

\( 40 q + 2 q^{2} - 20 q^{4} + 4 q^{5} - 4 q^{8} - 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(494, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
494.2.g.a	$494$	$2$	494.g	13.c	$3$	$2$	$1$	$3.945$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-2\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
494.2.g.b	$494$	$2$	494.g	13.c	$3$	$6$	$3$	$3.945$	6.0.771147.1	None		$2$	$0$	\(-3\)	\(2\)	\(4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots\)
494.2.g.c	$494$	$2$	494.g	13.c	$3$	$6$	$3$	$3.945$	6.0.34415307.1	None		$2$	$0$	\(3\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{4})q^{2}+\beta _{1}q^{3}+\beta _{4}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
494.2.g.d	$494$	$2$	494.g	13.c	$3$	$6$	$3$	$3.945$	6.0.34415307.1	None		$2$	$0$	\(3\)	\(0\)	\(4\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{4})q^{2}+\beta _{1}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
494.2.g.e	$494$	$2$	494.g	13.c	$3$	$8$	$4$	$3.945$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(4\)	\(2\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(1-\beta _{1}+\beta _{5})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
494.2.g.f	$494$	$2$	494.g	13.c	$3$	$12$	$6$	$3.945$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-6\)	\(-2\)	\(4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{7}q^{2}-\beta _{1}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(494, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(494, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(247, [\chi])\)\(^{\oplus 2}\)