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

• Label: 3380.1.bq
• Level: $3380$
• Weight: $1$
• Character orbit: 3380.bq
• Rep. character: $\chi_{3380}(259,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $546$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3380.bq (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3380 \)
Character field:			\(\Q(\zeta_{26})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(546\)
Trace bound:			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	72	72	0
Cusp forms	24	24	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	24	0	0	0

Trace form

\( 24 q - 2 q^{4} + 2 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3380.1.bq.a	$3380$	$1$	3380.bq	3380.aq	$26$	$12$	$1$	$1.687$	\(\Q(\zeta_{26})\)	$D_{26}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{26}^{10}q^{2}-\zeta_{26}^{7}q^{4}-\zeta_{26}^{2}q^{5}+\cdots\)
3380.1.bq.b	$3380$	$1$	3380.bq	3380.aq	$26$	$12$	$1$	$1.687$	\(\Q(\zeta_{26})\)	$D_{26}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-\zeta_{26}^{10}q^{2}-\zeta_{26}^{7}q^{4}-\zeta_{26}^{9}q^{5}+\cdots\)