Space of modular forms of level 201, weight 2, and Character 201.f

• Label: 201.2.f
• Level: $201$
• Weight: $2$
• Character orbit: 201.f
• Rep. character: $\chi_{201}(38,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $42$
• Newform subspaces: $2$
• Sturm bound: $45$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.f (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(45\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(201, [\chi])\).

	Total	New	Old
Modular forms	50	50	0
Cusp forms	42	42	0
Eisenstein series	8	8	0

Trace form

\( 42 q - 22 q^{4} - 2 q^{6} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(201, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
201.2.f.a	$201$	$2$	201.f	201.f	$6$	$2$	$1$	$1.605$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(1-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(4-2\zeta_{6})q^{7}+\cdots\)
201.2.f.b	$201$	$2$	201.f	201.f	$6$	$40$	$20$	$1.605$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{6}]$