Space of modular forms of level 3113, weight 1, and Character 3113.l

• Label: 3113.1.l
• Level: $3113$
• Weight: $1$
• Character orbit: 3113.l
• Rep. character: $\chi_{3113}(565,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $284$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3113 = 11 \cdot 283 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3113.l (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3113 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(284\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3113, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	12	12	0
Eisenstein series	8	8	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

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

Decomposition of \(S_{1}^{\mathrm{new}}(3113, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3113.1.l.a	$3113$	$1$	3113.l	3113.l	$10$	$4$	$1$	$1.554$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-283}) \)	None		✓			3113.1.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{10}q^{4}-\zeta_{10}q^{7}-\zeta_{10}^{3}q^{9}-\zeta_{10}^{3}q^{11}+\cdots\)
3113.1.l.b	$3113$	$1$	3113.l	3113.l	$10$	$8$	$2$	$1.554$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-283}) \)	None		✓	✓		3113.1.l.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\zeta_{30}^{3}q^{4}+\zeta_{30}^{3}q^{7}-\zeta_{30}^{9}q^{9}+\cdots\)