Space of modular forms of level 49, weight 2, and Character 49.g

• Label: 49.2.g
• Level: $49$
• Weight: $2$
• Character orbit: 49.g
• Rep. character: $\chi_{49}(2,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.g (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(49, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	48	48	0
Eisenstein series	24	24	0

Trace form

\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(49, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
49.2.g.a	$49$	$2$	49.g	49.g	$21$	$48$	$4$	$0.391$		None		$2$	$0$	\(-13\)	\(-14\)	\(-14\)	\(-14\)		$\mathrm{SU}(2)[C_{21}]$