Space of modular forms of level 2808, weight 1, and Character 2808.fi

• Label: 2808.1.fi
• Level: $2808$
• Weight: $1$
• Character orbit: 2808.fi
• Rep. character: $\chi_{2808}(259,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $504$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 2808 = 2^{3} \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2808.fi (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2808 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(504\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2808, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	36	36	0
Eisenstein series	24	24	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	36	0	0	0

Trace form

\( 36 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2808, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2808.1.fi.a	$2808$	$1$	2808.fi	2808.ei	$18$	$18$	$3$	$1.401$	\(\Q(\zeta_{54})\)	$D_{27}$	\(\Q(\sqrt{-26}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{54}^{24}q^{2}-\zeta_{54}^{7}q^{3}-\zeta_{54}^{21}q^{4}+\cdots\)
2808.1.fi.b	$2808$	$1$	2808.fi	2808.ei	$18$	$18$	$3$	$1.401$	\(\Q(\zeta_{54})\)	$D_{27}$	\(\Q(\sqrt{-26}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{54}^{24}q^{2}-\zeta_{54}^{7}q^{3}-\zeta_{54}^{21}q^{4}+\cdots\)