Space of modular forms of level 2793, weight 1, and Character 2793.ci

• Label: 2793.1.ci
• Level: $2793$
• Weight: $1$
• Character orbit: 2793.ci
• Rep. character: $\chi_{2793}(557,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $373$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2793.ci (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 399 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(373\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2793, [\chi])\).

	Total	New	Old
Modular forms	114	54	60
Cusp forms	18	6	12
Eisenstein series	96	48	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - 6 q^{12} + 3 q^{13} + 3 q^{19} + 3 q^{27} - 3 q^{43} + 3 q^{52} + 3 q^{61} - 3 q^{64} - 3 q^{67} - 6 q^{73} + 3 q^{75} + 6 q^{79} - 3 q^{93}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2793, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2793.1.ci.a	$2793$	$1$	2793.ci	399.ba	$18$	$6$	$1$	$1.394$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-3}) \)	None			✓	✓	399.1.ca.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{4}q^{3}-\zeta_{18}^{5}q^{4}+\zeta_{18}^{8}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2793, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2793, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)