Space of modular forms of level 261, weight 3, and Character 261.t

• Label: 261.3.t
• Level: $261$
• Weight: $3$
• Character orbit: 261.t
• Rep. character: $\chi_{261}(20,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $696$
• Newform subspaces: $1$
• Sturm bound: $90$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.t (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 261 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(90\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(261, [\chi])\).

	Total	New	Old
Modular forms	744	744	0
Cusp forms	696	696	0
Eisenstein series	48	48	0

Trace form

\( 696 q - 15 q^{2} - 10 q^{3} - 117 q^{4} - 15 q^{5} + 32 q^{6} - 5 q^{7} - 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(261, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
261.3.t.a	$261$	$3$	261.t	261.t	$42$	$696$	$58$	$7.112$		None		$4$	$0$	\(-15\)	\(-10\)	\(-15\)	\(-5\)		$\mathrm{SU}(2)[C_{42}]$