Space of modular forms of level 196, weight 2, and Character 196.p

• Label: 196.2.p
• Level: $196$
• Weight: $2$
• Character orbit: 196.p
• Rep. character: $\chi_{196}(3,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $312$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.p (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 196 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(196, [\chi])\).

	Total	New	Old
Modular forms	360	360	0
Cusp forms	312	312	0
Eisenstein series	48	48	0

Trace form

\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(196, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
196.2.p.a	$196$	$2$	196.p	196.p	$42$	$312$	$26$	$1.565$		None		✓	196.2.p.a	$4$	$0$	\(-13\)	\(0\)	\(-22\)	\(0\)		$\mathrm{SU}(2)[C_{42}]$