Space of modular forms of level 49, weight 4, and Character 49.e

• Label: 49.4.e
• Level: $49$
• Weight: $4$
• Character orbit: 49.e
• Rep. character: $\chi_{49}(8,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $78$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(49, [\chi])\).

	Total	New	Old
Modular forms	90	90	0
Cusp forms	78	78	0
Eisenstein series	12	12	0

Trace form

\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(49, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
49.4.e.a	$49$	$4$	49.e	49.e	$7$	$78$	$13$	$2.891$		None		$2$	$0$	\(-5\)	\(-5\)	\(-23\)	\(0\)		$\mathrm{SU}(2)[C_{7}]$