Space of modular forms of level 164, weight 2, and trivial character

• Label: 164.2.a
• Level: $164$
• Weight: $2$
• Character orbit: 164.a
• Rep. character: $\chi_{164}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $42$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	164.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(42\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(164))\).

	Total	New	Old
Modular forms	24	4	20
Cusp forms	19	4	15
Eisenstein series	5	0	5

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
\(-\)	\(+\)	$-$	\(4\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(4\)

Trace form

\( 4 q + 2 q^{3} + 4 q^{5} + 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(164))\) 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
164.2.a.a	$164$	$2$	164.a	1.a	$1$	$4$	$4$	$1.310$	4.4.25808.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(4\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{3}+(2-\beta _{2}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(164))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(164)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 2}\)