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

• Label: 621.1.f
• Level: $621$
• Weight: $1$
• Character orbit: 621.f
• Rep. character: $\chi_{621}(91,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• 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.f (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 207 \)
Character field:			\(\Q(\zeta_{6})\)
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	10	20
Cusp forms	18	6	12
Eisenstein series	12	4	8

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

\( 6 q - 3 q^{4} + 6 q^{8} - 3 q^{16} + 3 q^{23} - 3 q^{25} - 12 q^{26} - 3 q^{32} - 3 q^{49} + 3 q^{52} + 3 q^{58} - 3 q^{59} + 6 q^{62} - 6 q^{82} + 3 q^{92} + 3 q^{94}+O(q^{100}) \)

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.f.a	$621$	$1$	621.f	207.f	$6$	$6$	$3$	$0.310$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-23}) \)	None			✓	✓	207.1.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$		\(q+(\zeta_{18}-\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(621, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(621, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)