Space of modular forms of level 643, weight 2, and trivial character

• Label: 643.2.a
• Level: $643$
• Weight: $2$
• Character orbit: 643.a
• Rep. character: $\chi_{643}(1,\cdot)$
• Character field: $\Q$
• Dimension: $53$
• Newform subspaces: $3$
• Sturm bound: $107$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 643 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	643.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(107\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(643))\).

	Total	New	Old
Modular forms	54	54	0
Cusp forms	53	53	0
Eisenstein series	1	1	0

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

\(643\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(24\)	\(24\)	\(0\)		\(24\)	\(24\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(30\)	\(30\)	\(0\)		\(29\)	\(29\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

53 * q - 4 * q^3 + 54 * q^4 - 2 * q^5 - 2 * q^7 + 6 * q^8 + 43 * q^9 + 12 * q^10 - 4 * q^11 - 14 * q^12 - 2 * q^13 - 4 * q^14 - 12 * q^15 + 68 * q^16 - 10 * q^17 - 18 * q^18 - 4 * q^19 - 18 * q^20 - 26 * q^21 - 10 * q^22 - 4 * q^23 - 14 * q^24 + 53 * q^25 + 8 * q^26 - 10 * q^27 - 8 * q^28 - 8 * q^29 - 8 * q^30 - 6 * q^31 - 18 * q^32 + 4 * q^33 + 12 * q^34 + 4 * q^35 + 38 * q^36 + 4 * q^37 - 4 * q^38 - 14 * q^39 + 22 * q^40 - 4 * q^41 - 14 * q^42 + 2 * q^43 - 2 * q^44 - 36 * q^45 - 8 * q^47 + 10 * q^48 + 37 * q^49 - 24 * q^50 - 18 * q^51 - 18 * q^52 + 2 * q^53 + 50 * q^54 + 12 * q^55 - 6 * q^56 - 48 * q^57 + 54 * q^58 - 6 * q^59 - 50 * q^60 - 32 * q^62 - 28 * q^63 + 108 * q^64 + 10 * q^65 - 32 * q^66 - 48 * q^68 - 26 * q^69 - 12 * q^70 - 26 * q^71 - 68 * q^72 - 24 * q^73 + 44 * q^74 - 44 * q^75 - 14 * q^76 - 66 * q^77 - 40 * q^78 - 18 * q^79 - 76 * q^80 - 27 * q^81 + 4 * q^82 + 6 * q^83 - 74 * q^84 - 14 * q^85 - 4 * q^86 - 8 * q^87 + 22 * q^88 + 24 * q^89 + 84 * q^90 - 30 * q^91 - 6 * q^92 - 8 * q^93 + 28 * q^94 - 6 * q^95 - 10 * q^96 + 12 * q^97 - 14 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(643))\) 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		643
643.2.a.a	$643$	$2$	643.a	1.a	$1$	$1$	$1$	$5.134$	\(\Q\)	None	✓	✓			643.2.a.a	$1$	$2$	\(-1\)	\(-2\)	\(-2\)	\(-3\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-q^{4}-2q^{5}+2q^{6}-3q^{7}+\cdots\)
643.2.a.b	$643$	$2$	643.a	1.a	$1$	$24$	$24$	$5.134$		None	✓	✓	✓	✓	643.2.a.b	$1$	$1$	\(-13\)	\(-7\)	\(-23\)	\(-10\)		$+$	$+$		$\mathrm{SU}(2)$
643.2.a.c	$643$	$2$	643.a	1.a	$1$	$28$	$28$	$5.134$		None	✓	✓	✓		643.2.a.c	$1$	$0$	\(14\)	\(5\)	\(23\)	\(11\)		$-$	$-$		$\mathrm{SU}(2)$