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

• Label: 201.2.m
• Level: $201$
• Weight: $2$
• Character orbit: 201.m
• Rep. character: $\chi_{201}(4,\cdot)$
• Character field: $\Q(\zeta_{33})$
• Dimension: $220$
• Newform subspaces: $2$
• Sturm bound: $45$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.m (of order \(33\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 67 \)
Character field:			\(\Q(\zeta_{33})\)
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	500	220	280
Cusp forms	420	220	200
Eisenstein series	80	0	80

Trace form

\( 220 q + 4 q^{2} - 2 q^{3} + 14 q^{4} + 6 q^{7} - 78 q^{8} - 22 q^{9} + O(q^{10}) \)

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.m.a	$201$	$2$	201.m	67.g	$33$	$100$	$5$	$1.605$		None		$2$	$0$	\(2\)	\(10\)	\(-2\)	\(1\)		$\mathrm{SU}(2)[C_{33}]$
201.2.m.b	$201$	$2$	201.m	67.g	$33$	$120$	$6$	$1.605$		None		$2$	$0$	\(2\)	\(-12\)	\(2\)	\(5\)		$\mathrm{SU}(2)[C_{33}]$

Decomposition of \(S_{2}^{\mathrm{old}}(201, [\chi])\) into lower level spaces

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