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

• Label: 261.2.r
• Level: $261$
• Weight: $2$
• Character orbit: 261.r
• Rep. character: $\chi_{261}(8,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $120$
• 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.r (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 87 \)
Character field:			\(\Q(\zeta_{28})\)
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	408	120	288
Cusp forms	312	120	192
Eisenstein series	96	0	96

Trace form

\( 120 q + O(q^{10}) \)

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.r.a	$261$	$2$	261.r	87.k	$28$	$120$	$10$	$2.084$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$

Decomposition of \(S_{2}^{\mathrm{old}}(261, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(261, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)