Space of modular forms of level 49, weight 2, and trivial character

• Label: 49.2.a
• Level: $49$
• Weight: $2$
• Character orbit: 49.a
• Rep. character: $\chi_{49}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(49))\).

	Total	New	Old
Modular forms	8	6	2
Cusp forms	1	1	0
Eisenstein series	7	5	2

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

\(7\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(3\)	\(2\)	\(1\)		\(0\)	\(0\)	\(0\)		\(3\)	\(2\)	\(1\)
\(-\)		\(5\)	\(4\)	\(1\)		\(1\)	\(1\)	\(0\)		\(4\)	\(3\)	\(1\)

Trace form

q + q^2 - q^4 - 3 * q^8 - 3 * q^9 + 4 * q^11 - q^16 - 3 * q^18 + 4 * q^22 + 8 * q^23 - 5 * q^25 + 2 * q^29 + 5 * q^32 + 3 * q^36 - 6 * q^37 - 12 * q^43 - 4 * q^44 + 8 * q^46 - 5 * q^50 - 10 * q^53 + 2 * q^58 + 7 * q^64 + 4 * q^67 + 16 * q^71 + 9 * q^72 - 6 * q^74 + 8 * q^79 + 9 * q^81 - 12 * q^86 - 12 * q^88 - 8 * q^92 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(49))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7
49.2.a.a	$49$	$2$	49.a	1.a	$1$	$1$	$1$	$0.391$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	✓	✓	✓	49.2.a.a	$2$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+q^{2}-q^{4}-3q^{8}-3q^{9}+4q^{11}+\cdots\)