Space of Modular Forms of Level 49, Weight 2, and Trivial Character

• Label: 49.2.a
• Level: 49
• Weight: 2
• Character orbit: 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.

\(7\)	Dim.
\(-\)	\(1\)

Trace form

\( q + q^{2} - q^{4} - 3q^{8} - 3q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(49))\) into newform subspaces

Label	Dim.	\(A\)	Field	CM	Traces					A-L signs	$q$-expansion
					\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)		7
49.2.a.a	\(1\)	\(0.391\)	\(\Q\)	\(\Q(\sqrt{-7}) \)	\(1\)	\(0\)	\(0\)	\(0\)		\(-\)	\(q+q^{2}-q^{4}-3q^{8}-3q^{9}+4q^{11}+\cdots\)