Space of modular forms of level 82, weight 2, and trivial character

• Label: 82.2.a
• Level: $82$
• Weight: $2$
• Character orbit: 82.a
• Rep. character: $\chi_{82}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $21$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	82.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(21\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(82))\).

	Total	New	Old
Modular forms	12	3	9
Cusp forms	9	3	6
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.

\(2\)	\(41\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(1\)
\(-\)	\(+\)	$-$	\(2\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(2\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(82))\) 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	41
82.2.a.a	$82$	$2$	82.a	1.a	$1$	$1$	$1$	$0.655$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-4q^{7}+\cdots\)
82.2.a.b	$82$	$2$	82.a	1.a	$1$	$2$	$2$	$0.655$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}-2\beta q^{5}+\beta q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(82))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(82)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 2}\)