Space of modular forms of level 644, weight 2, and Character 644.i

• Label: 644.2.i
• Level: $644$
• Weight: $2$
• Character orbit: 644.i
• Rep. character: $\chi_{644}(93,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(644, [\chi])\).

	Total	New	Old
Modular forms	204	28	176
Cusp forms	180	28	152
Eisenstein series	24	0	24

Trace form

\( 28 q + 2 q^{3} + 10 q^{7} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(644, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
644.2.i.a	$644$	$2$	644.i	7.c	$3$	$14$	$7$	$5.142$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(-3\)	\(-2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{10}q^{3}+(-\beta _{2}-\beta _{11})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
644.2.i.b	$644$	$2$	644.i	7.c	$3$	$14$	$7$	$5.142$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(5\)	\(2\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}-\beta _{7})q^{3}+(-\beta _{3}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(644, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(644, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)