Space of modular forms of level 3380, weight 1, and Character 3380.cs

• Label: 3380.1.cs
• Level: $3380$
• Weight: $1$
• Character orbit: 3380.cs
• Rep. character: $\chi_{3380}(7,\cdot)$
• Character field: $\Q(\zeta_{156})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $546$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3380.cs (of order \(156\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3380 \)
Character field:			\(\Q(\zeta_{156})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(546\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3380, [\chi])\).

	Total	New	Old
Modular forms	240	240	0
Cusp forms	48	48	0
Eisenstein series	192	192	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	48	0	0	0

Trace form

\( 48 q - 2 q^{4} + 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3380, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3380.1.cs.a	$3380$	$1$	3380.cs	3380.bs	$156$	$48$	$1$	$1.687$	\(\Q(\zeta_{156})\)	$D_{156}$	\(\Q(\sqrt{-1}) \)	None		✓	3380.1.cs.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\zeta_{156}^{41}q^{2}-\zeta_{156}^{4}q^{4}-\zeta_{156}^{46}q^{5}+\cdots\)