Space of modular forms of level 261, weight 2, and Character 261.u

• Label: 261.2.u
• Level: $261$
• Weight: $2$
• Character orbit: 261.u
• Rep. character: $\chi_{261}(4,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $336$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.u (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 261 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(261, [\chi])\).

	Total	New	Old
Modular forms	384	384	0
Cusp forms	336	336	0
Eisenstein series	48	48	0

Trace form

\( 336 q - 7 q^{2} - 14 q^{3} - 31 q^{4} - 9 q^{5} + 20 q^{6} - 5 q^{7} - 70 q^{8} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(261, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
261.2.u.a	$261$	$2$	261.u	261.u	$42$	$336$	$28$	$2.084$		None		$4$	$0$	\(-7\)	\(-14\)	\(-9\)	\(-5\)		$\mathrm{SU}(2)[C_{42}]$