Space of modular forms of level 111, weight 2, and Character 111.k

• Label: 111.2.k
• Level: $111$
• Weight: $2$
• Character orbit: 111.k
• Rep. character: $\chi_{111}(7,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $42$
• Newform subspaces: $2$
• Sturm bound: $25$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	111.k (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(25\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(111, [\chi])\).

	Total	New	Old
Modular forms	90	42	48
Cusp forms	66	42	24
Eisenstein series	24	0	24

Trace form

\( 42 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 3 q^{7} - 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(111, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
111.2.k.a	$111$	$2$	111.k	37.f	$9$	$18$	$3$	$0.886$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{7}q^{2}+(\beta _{9}+\beta _{13})q^{3}+(\beta _{13}+\beta _{16}+\cdots)q^{4}+\cdots\)
111.2.k.b	$111$	$2$	111.k	37.f	$9$	$24$	$4$	$0.886$		None		$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(-9\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(111, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(111, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)