Space of modular forms of level 3311, weight 1, and Character 3311.cm

• Label: 3311.1.cm
• Level: $3311$
• Weight: $1$
• Character orbit: 3311.cm
• Rep. character: $\chi_{3311}(251,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $352$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 3311 = 7 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3311.cm (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3311 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(352\)
Trace bound:			\(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3311, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	16	16	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + 4 q^{2} + 2 q^{7} - 14 q^{8} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3311, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3311.1.cm.a	$3311$	$1$	3311.cm	3311.bm	$30$	$8$	$1$	$1.652$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(1\)	$1$		\(q+(\zeta_{30}^{2}+\zeta_{30}^{4})q^{2}+(\zeta_{30}^{4}+\zeta_{30}^{6}+\cdots)q^{4}+\cdots\)
3311.1.cm.b	$3311$	$1$	3311.cm	3311.bm	$30$	$8$	$1$	$1.652$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(1\)	$1$		\(q+(-\zeta_{30}^{7}+\zeta_{30}^{14})q^{2}+(\zeta_{30}^{6}-\zeta_{30}^{13}+\cdots)q^{4}+\cdots\)