Space of modular forms of level 1308, weight 1, and Character 1308.br

• Label: 1308.1.br
• Level: $1308$
• Weight: $1$
• Character orbit: 1308.br
• Rep. character: $\chi_{1308}(5,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $18$
• Newform subspaces: $1$
• Sturm bound: $220$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1308 = 2^{2} \cdot 3 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1308.br (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 327 \)
Character field:			\(\Q(\zeta_{54})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(220\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1308, [\chi])\).

	Total	New	Old
Modular forms	126	18	108
Cusp forms	18	18	0
Eisenstein series	108	0	108

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	18	0	0	0

Trace form

\( 18 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1308, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1308.1.br.a	$1308$	$1$	1308.br	327.v	$54$	$18$	$1$	$0.653$	\(\Q(\zeta_{54})\)	$D_{27}$	\(\Q(\sqrt{-3}) \)	None		✓	1308.1.br.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{54}^{22}q^{3}+(-\zeta_{54}^{5}+\zeta_{54}^{6})q^{7}+\cdots\)