Space of modular forms of level 142, weight 2, and trivial character

• Label: 142.2.a
• Level: $142$
• Weight: $2$
• Character orbit: 142.a
• Rep. character: $\chi_{142}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $5$
• Sturm bound: $36$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 142 = 2 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	142.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(36\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(142))\).

	Total	New	Old
Modular forms	20	5	15
Cusp forms	17	5	12
Eisenstein series	3	0	3

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

\(2\)	\(71\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(2\)
\(-\)	\(+\)	$-$	\(1\)
\(-\)	\(-\)	$+$	\(1\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(3\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(142))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	71
142.2.a.a	$142$	$2$	142.a	1.a	$1$	$1$	$1$	$1.134$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
142.2.a.b	$142$	$2$	142.a	1.a	$1$	$1$	$1$	$1.134$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-q^{8}-3q^{9}-2q^{10}+\cdots\)
142.2.a.c	$142$	$2$	142.a	1.a	$1$	$1$	$1$	$1.134$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(3\)	\(2\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}+2q^{5}-3q^{6}-3q^{7}+\cdots\)
142.2.a.d	$142$	$2$	142.a	1.a	$1$	$1$	$1$	$1.134$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-3\)	\(-4\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-4q^{5}-3q^{6}-3q^{7}+\cdots\)
142.2.a.e	$142$	$2$	142.a	1.a	$1$	$1$	$1$	$1.134$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(142))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(142)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(71))\)\(^{\oplus 2}\)