Space of modular forms of level 164, weight 2, and Character 164.b

• Label: 164.2.b
• Level: $164$
• Weight: $2$
• Character orbit: 164.b
• Rep. character: $\chi_{164}(81,\cdot)$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(42\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(164, [\chi])\).

	Total	New	Old
Modular forms	24	4	20
Cusp forms	18	4	14
Eisenstein series	6	0	6

Trace form

\( 4 q - 4 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(164, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
164.2.b.a	$164$	$2$	164.b	41.b	$2$	$4$	$4$	$1.310$	4.0.25088.1	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-\beta _{3}q^{7}+\beta _{2}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(164, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(164, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 2}\)