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

• Label: 201.4.i
• Level: $201$
• Weight: $4$
• Character orbit: 201.i
• Rep. character: $\chi_{201}(22,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $340$
• Newform subspaces: $2$
• Sturm bound: $90$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.i (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 67 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(90\)
Trace bound:			\(3\)
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	340	360
Cusp forms	660	340	320
Eisenstein series	40	0	40

Trace form

\( 340 q + 4 q^{2} - 156 q^{4} - 4 q^{7} - 414 q^{8} - 306 q^{9} + O(q^{10}) \)

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.i.a	$201$	$4$	201.i	67.e	$11$	$170$	$17$	$11.859$		None		$2$	$0$	\(2\)	\(-51\)	\(4\)	\(-16\)		$\mathrm{SU}(2)[C_{11}]$
201.4.i.b	$201$	$4$	201.i	67.e	$11$	$170$	$17$	$11.859$		None		$2$	$0$	\(2\)	\(51\)	\(-4\)	\(12\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{4}^{\mathrm{old}}(201, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(201, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)