Space of modular forms of level 166, weight 2, and trivial character

• Label: 166.2.a
• Level: $166$
• Weight: $2$
• Character orbit: 166.a
• Rep. character: $\chi_{166}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $42$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 166 = 2 \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	166.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(42\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(166))\).

	Total	New	Old
Modular forms	23	6	17
Cusp forms	20	6	14
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.

\(2\)	\(83\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(2\)
\(-\)	\(+\)	$-$	\(3\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(5\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(166))\) 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	83
166.2.a.a	$166$	$2$	166.a	1.a	$1$	$1$	$1$	$1.326$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
166.2.a.b	$166$	$2$	166.a	1.a	$1$	$2$	$2$	$1.326$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-2\)	\(-2\)	\(3\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2\beta q^{3}+q^{4}+(2-\beta )q^{5}+2\beta q^{6}+\cdots\)
166.2.a.c	$166$	$2$	166.a	1.a	$1$	$3$	$3$	$1.326$	3.3.229.1	None	✓	$1$	$0$	\(3\)	\(1\)	\(-1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(166))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(166)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(83))\)\(^{\oplus 2}\)