Space of modular forms of level 644, weight 2, and trivial character

• Label: 644.2.a
• Level: $644$
• Weight: $2$
• Character orbit: 644.a
• Rep. character: $\chi_{644}(1,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(644))\).

	Total	New	Old
Modular forms	102	12	90
Cusp forms	91	12	79
Eisenstein series	11	0	11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(7\)	\(23\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	$+$	\(1\)
\(-\)	\(-\)	\(+\)	$+$	\(1\)
\(-\)	\(-\)	\(-\)	$-$	\(5\)
Plus space			\(+\)	\(2\)
Minus space			\(-\)	\(10\)

Trace form

\( 12 q + 4 q^{3} + 4 q^{5} + 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(644))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	23
644.2.a.a	$644$	$2$	644.a	1.a	$1$	$1$	$1$	$5.142$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}-2q^{9}-2q^{11}-3q^{13}+\cdots\)
644.2.a.b	$644$	$2$	644.a	1.a	$1$	$1$	$1$	$5.142$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}-2q^{9}-2q^{11}+\cdots\)
644.2.a.c	$644$	$2$	644.a	1.a	$1$	$5$	$5$	$5.142$	5.5.8580816.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
644.2.a.d	$644$	$2$	644.a	1.a	$1$	$5$	$5$	$5.142$	5.5.6963152.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(2\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{5}-q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(644))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(644)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 2}\)