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

• Label: 164.2.o
• Level: $164$
• Weight: $2$
• Character orbit: 164.o
• Rep. character: $\chi_{164}(7,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $304$
• Newform subspaces: $2$
• Sturm bound: $42$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	164.o (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 164 \)
Character field:			\(\Q(\zeta_{40})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(42\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	368	368	0
Cusp forms	304	304	0
Eisenstein series	64	64	0

Trace form

\( 304 q - 16 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 16 q^{8} - 40 q^{9} + O(q^{10}) \)

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.o.a	$164$	$2$	164.o	164.o	$40$	$16$	$1$	$1.310$	\(\Q(\zeta_{40})\)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{40}]$	\(q+(\zeta_{40}^{2}-\zeta_{40}^{6}+\zeta_{40}^{8}+\zeta_{40}^{10}+\cdots)q^{2}+\cdots\)
164.2.o.b	$164$	$2$	164.o	164.o	$40$	$288$	$18$	$1.310$		None		$4$	$0$	\(-12\)	\(0\)	\(-32\)	\(0\)		$\mathrm{SU}(2)[C_{40}]$