Space of modular forms of level 201, weight 4, and Character 201.j

• Label: 201.4.j
• Level: $201$
• Weight: $4$
• Character orbit: 201.j
• Rep. character: $\chi_{201}(5,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $660$
• Newform subspaces: $2$
• Sturm bound: $90$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.j (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(90\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(201, [\chi])\).

	Total	New	Old
Modular forms	700	700	0
Cusp forms	660	660	0
Eisenstein series	40	40	0

Trace form

\( 660 q - 11 q^{3} - 274 q^{4} + 35 q^{6} - 22 q^{7} + 21 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(201, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
201.4.j.a	$201$	$4$	201.j	201.j	$22$	$20$	$2$	$11.859$	\(\Q(\zeta_{33})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{10}$	$\mathrm{U}(1)[D_{22}]$	\(q+\zeta_{33}^{18}q^{3}+(8+8\zeta_{33}+8\zeta_{33}^{2}+\cdots)q^{4}+\cdots\)
201.4.j.b	$201$	$4$	201.j	201.j	$22$	$640$	$64$	$11.859$		None		$4$	$0$	\(0\)	\(-11\)	\(0\)	\(-22\)		$\mathrm{SU}(2)[C_{22}]$