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

• Label: 261.2.e
• Level: $261$
• Weight: $2$
• Character orbit: 261.e
• Rep. character: $\chi_{261}(88,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	64	56	8
Cusp forms	56	56	0
Eisenstein series	8	0	8

Trace form

\( 56 q - 2 q^{2} - 4 q^{3} - 28 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 12 q^{8} - 8 q^{9} + O(q^{10}) \)

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.e.a	$261$	$2$	261.e	9.c	$3$	$22$	$11$	$2.084$		None		$2$	$0$	\(-1\)	\(-2\)	\(1\)	\(7\)		$\mathrm{SU}(2)[C_{3}]$
261.2.e.b	$261$	$2$	261.e	9.c	$3$	$34$	$17$	$2.084$		None		$2$	$0$	\(-1\)	\(-2\)	\(1\)	\(-9\)		$\mathrm{SU}(2)[C_{3}]$