Space of modular forms of level 621, weight 1, and Character 621.k

• Label: 621.1.k
• Level: $621$
• Weight: $1$
• Character orbit: 621.k
• Rep. character: $\chi_{621}(22,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $18$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 621 = 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	621.k (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 621 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(621, [\chi])\).

	Total	New	Old
Modular forms	30	30	0
Cusp forms	18	18	0
Eisenstein series	12	12	0

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

\( 18 q - 9 q^{12} + 18 q^{24} - 18 q^{26} + 18 q^{32} - 9 q^{48} - 9 q^{52} - 9 q^{58} - 9 q^{59} - 9 q^{64} - 9 q^{87} - 9 q^{94}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(621, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
621.1.k.a	$621$	$1$	621.k	621.k	$18$	$18$	$3$	$0.310$	\(\Q(\zeta_{54})\)	$D_{27}$	\(\Q(\sqrt{-23}) \)	None		✓	✓	✓	621.1.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{54}+\zeta_{54}^{20})q^{2}-\zeta_{54}^{5}q^{3}+\cdots\)