Space of modular forms of level 644, weight 1, and Character 644.h

• Label: 644.1.h
• Level: $644$
• Weight: $1$
• Character orbit: 644.h
• Rep. character: $\chi_{644}(643,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	644.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 644 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(644, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

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 - 2 * q^2 + 6 * q^4 - 2 * q^8 + 2 * q^9 + 6 * q^16 - 6 * q^18 + 2 * q^25 - 4 * q^29 - 2 * q^32 + 2 * q^36 + 6 * q^49 - 6 * q^50 - 4 * q^58 + 6 * q^64 - 6 * q^72 - 4 * q^77 - 2 * q^81 - 8 * q^85 - 8 * q^93 - 2 * q^98

Decomposition of \(S_{1}^{\mathrm{new}}(644, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
644.1.h.a	$644$	$1$	644.h	644.h	$2$	$1$	$1$	$0.321$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-161}) \)	\(\Q(\sqrt{23}) \)	✓	✓			644.1.h.a	$4$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{9}+2q^{11}+\cdots\)
644.1.h.b	$644$	$1$	644.h	644.h	$2$	$1$	$1$	$0.321$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-161}) \)	\(\Q(\sqrt{23}) \)	✓	✓			644.1.h.a	$4$	$0$	\(1\)	\(0\)	\(0\)	\(1\)	$1$		\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{9}-2q^{11}+\cdots\)
644.1.h.c	$644$	$1$	644.h	644.h	$2$	$2$	$2$	$0.321$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-161}) \)	None	✓	✓			644.1.h.c	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-q^{2}-\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}-q^{7}+\cdots\)
644.1.h.d	$644$	$1$	644.h	644.h	$2$	$2$	$2$	$0.321$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-161}) \)	None	✓	✓			644.1.h.c	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)	$1$		\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+q^{7}+\cdots\)