Space of modular forms of level 62, weight 2, and trivial character

• Label: 62.2.a
• Level: $62$
• Weight: $2$
• Character orbit: 62.a
• Rep. character: $\chi_{62}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(62))\).

	Total	New	Old
Modular forms	10	3	7
Cusp forms	7	3	4
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.

\(2\)	\(31\)	Fricke	Dim
\(+\)	\(-\)	$-$	\(2\)
\(-\)	\(+\)	$-$	\(1\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(3\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(62))\) 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	31
62.2.a.a	$62$	$2$	62.a	1.a	$1$	$1$	$1$	$0.495$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots\)
62.2.a.b	$62$	$2$	62.a	1.a	$1$	$2$	$2$	$0.495$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}-2\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(62))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(62)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)