Space of modular forms of level 2011, weight 1, and Character 2011.b

• Label: 2011.1.b
• Level: $2011$
• Weight: $1$
• Character orbit: 2011.b
• Rep. character: $\chi_{2011}(2010,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $1$
• Sturm bound: $167$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2011 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2011.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2011 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(167\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2011, [\chi])\).

	Total	New	Old
Modular forms	4	4	0
Cusp forms	3	3	0
Eisenstein series	1	1	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	3	0	0	0

Trace form

\( 3 q + 3 q^{4} - q^{5} + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2011, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2011.1.b.a	$2011$	$1$	2011.b	2011.b	$2$	$3$	$3$	$1.004$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-2011}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{4}-\beta _{1}q^{5}+q^{9}+(-1+\beta _{1}-\beta _{2})q^{13}+\cdots\)