Space of modular forms of level 139, weight 2, and trivial character

• Label: 139.2.a
• Level: $139$
• Weight: $2$
• Character orbit: 139.a
• Rep. character: $\chi_{139}(1,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $3$
• Sturm bound: $23$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	139.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(23\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(139))\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	11	11	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.

\(139\)	Dim
\(+\)	\(3\)
\(-\)	\(8\)

Trace form

\( 11 q - 2 q^{3} + 8 q^{4} + 2 q^{5} - 6 q^{6} - 2 q^{7} + 11 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(139))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		139
139.2.a.a	$139$	$2$	139.a	1.a	$1$	$1$	$1$	$1.110$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(2\)	\(-1\)	\(3\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}-q^{4}-q^{5}+2q^{6}+3q^{7}+\cdots\)
139.2.a.b	$139$	$2$	139.a	1.a	$1$	$3$	$3$	$1.110$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(-8\)	\(0\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
139.2.a.c	$139$	$2$	139.a	1.a	$1$	$7$	$7$	$1.110$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(-2\)	\(11\)	\(-5\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{1}-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)