Space of modular forms of level 621, weight 2, and Character 621.c

• Label: 621.2.c
• Level: $621$
• Weight: $2$
• Character orbit: 621.c
• Rep. character: $\chi_{621}(620,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 621 = 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	621.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(621, [\chi])\).

	Total	New	Old
Modular forms	78	32	46
Cusp forms	66	32	34
Eisenstein series	12	0	12

Trace form

\( 32 q - 36 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(621, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
621.2.c.a	$621$	$2$	621.c	69.c	$2$	$16$	$16$	$4.959$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			621.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}+(-1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)
621.2.c.b	$621$	$2$	621.c	69.c	$2$	$16$	$16$	$4.959$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			621.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{4}-\beta _{13}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(621, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(621, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)