Space of modular forms of level 261, weight 1, and Character 261.f

• Label: 261.1.f
• Level: $261$
• Weight: $1$
• Character orbit: 261.f
• Rep. character: $\chi_{261}(46,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	261.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(261, [\chi])\).

	Total	New	Old
Modular forms	12	6	6
Cusp forms	4	4	0
Eisenstein series	8	2	6

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	4	0

Trace form

\( 4 q - 4 q^{7} - 4 q^{10} + 4 q^{16} - 4 q^{25} + 4 q^{40} + 4 q^{43} - 4 q^{46} + 4 q^{55} + 4 q^{61} + 4 q^{70} - 4 q^{73} - 4 q^{79} - 4 q^{85} - 4 q^{88} - 4 q^{94}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(261, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
261.1.f.a	$261$	$1$	261.f	29.c	$4$	$4$	$2$	$0.130$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		✓	✓	✓	261.1.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q-\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)