Space of modular forms of level 1911, weight 1, and Character 1911.dx

• Label: 1911.1.dx
• Level: $1911$
• Weight: $1$
• Character orbit: 1911.dx
• Rep. character: $\chi_{1911}(74,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $261$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1911.dx (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1911 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(261\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1911, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	12	12	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	12	0	0	0

Trace form

\( 12 q + q^{3} - 2 q^{4} + q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1911, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1911.1.dx.a	$1911$	$1$	1911.dx	1911.cx	$42$	$12$	$1$	$0.954$	\(\Q(\zeta_{21})\)	$D_{21}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$1$		\(q+\zeta_{42}^{20}q^{3}+\zeta_{42}^{18}q^{4}+\zeta_{42}^{2}q^{7}+\cdots\)