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

• Label: 1911.1.w
• Level: $1911$
• Weight: $1$
• Character orbit: 1911.w
• Rep. character: $\chi_{1911}(116,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $6$
• Sturm bound: $261$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1911.w (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(261\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	60	44	16
Cusp forms	28	28	0
Eisenstein series	32	16	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	28	0	0	0

Trace form

\( 28 q - 10 q^{4} - 14 q^{9} + O(q^{10}) \)

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.w.a	$1911$	$1$	1911.w	273.w	$6$	$2$	$1$	$0.954$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \)	\(\Q(\sqrt{13}) \)		$8$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{12}+\cdots\)
1911.1.w.b	$1911$	$1$	1911.w	273.w	$6$	$2$	$1$	$0.954$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \)	\(\Q(\sqrt{13}) \)		$8$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{12}+\cdots\)
1911.1.w.c	$1911$	$1$	1911.w	273.w	$6$	$4$	$2$	$0.954$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-39}) \)	None		$8$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
1911.1.w.d	$1911$	$1$	1911.w	273.w	$6$	$4$	$2$	$0.954$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-39}) \)	None		$8$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}-\beta _{1}q^{5}+\cdots\)
1911.1.w.e	$1911$	$1$	1911.w	273.w	$6$	$8$	$4$	$0.954$	8.0.339738624.2	$D_{8}$	\(\Q(\sqrt{-39}) \)	None		$8$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$		\(q+\beta _{3}q^{2}+\beta _{5}q^{3}+(\beta _{5}-\beta _{6})q^{4}+\beta _{1}q^{5}+\cdots\)
1911.1.w.f	$1911$	$1$	1911.w	273.w	$6$	$8$	$4$	$0.954$	8.0.339738624.2	$D_{8}$	\(\Q(\sqrt{-39}) \)	None		$8$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$		\(q+\beta _{3}q^{2}-\beta _{5}q^{3}+(\beta _{5}-\beta _{6})q^{4}-\beta _{1}q^{5}+\cdots\)