Space of modular forms of level 1011, weight 1, and Character 1011.bf

• Label: 1011.1.bf
• Level: $1011$
• Weight: $1$
• Character orbit: 1011.bf
• Rep. character: $\chi_{1011}(47,\cdot)$
• Character field: $\Q(\zeta_{56})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1011 = 3 \cdot 337 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1011.bf (of order \(56\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1011 \)
Character field:			\(\Q(\zeta_{56})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1011, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	24	24	0
Eisenstein series	48	48	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q - 4 q^{4} + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1011, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1011.1.bf.a	$1011$	$1$	1011.bf	1011.af	$56$	$24$	$1$	$0.505$	\(\Q(\zeta_{56})\)	$D_{56}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$		\(q-\zeta_{56}^{15}q^{3}+\zeta_{56}^{8}q^{4}+(\zeta_{56}^{6}-\zeta_{56}^{16}+\cdots)q^{7}+\cdots\)