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

• Label: 261.2.g
• Level: $261$
• Weight: $2$
• Character orbit: 261.g
• Rep. character: $\chi_{261}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 87 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	68	20	48
Cusp forms	52	20	32
Eisenstein series	16	0	16

Trace form

\( 20 q + O(q^{10}) \)

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.g.a	$261$	$2$	261.g	87.f	$4$	$4$	$2$	$2.084$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
261.2.g.b	$261$	$2$	261.g	87.f	$4$	$8$	$4$	$2.084$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$3^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}+(2\beta _{2}+\beta _{6})q^{4}+(\beta _{4}-\beta _{7})q^{5}+\cdots\)
261.2.g.c	$261$	$2$	261.g	87.f	$4$	$8$	$4$	$2.084$	8.0.1871773696.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(2\beta _{3}+\beta _{5})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

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

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