Space of modular forms of level 676, weight 1, and Character 676.t

• Label: 676.1.t
• Level: $676$
• Weight: $1$
• Character orbit: 676.t
• Rep. character: $\chi_{676}(3,\cdot)$
• Character field: $\Q(\zeta_{78})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $91$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	676.t (of order \(78\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 676 \)
Character field:			\(\Q(\zeta_{78})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(91\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(676, [\chi])\).

	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

\( 24 q + q^{2} + q^{4} + 2 q^{5} - 2 q^{8} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(676, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
676.1.t.a	$676$	$1$	676.t	676.t	$78$	$24$	$1$	$0.337$	\(\Q(\zeta_{39})\)	$D_{39}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(1\)	\(0\)	\(2\)	\(0\)	$1$		\(q+\zeta_{78}^{8}q^{2}+\zeta_{78}^{16}q^{4}+(\zeta_{78}^{28}+\zeta_{78}^{38}+\cdots)q^{5}+\cdots\)