Space of modular forms of level 111, weight 1, and Character 111.h

• Label: 111.1.h
• Level: $111$
• Weight: $1$
• Character orbit: 111.h
• Rep. character: $\chi_{111}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	111.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 111 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(111, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	0
Eisenstein series	4	4	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

2 * q - q^3 + q^4 - q^7 - q^9 + q^12 - 3 * q^13 - q^16 - q^21 + q^25 + 2 * q^27 + q^28 - 2 * q^36 + 2 * q^37 + 3 * q^39 + 2 * q^48 - 3 * q^52 + 2 * q^63 - 2 * q^64 - q^67 + 2 * q^73 - 2 * q^75 - 3 * q^79 - q^81 - 2 * q^84 + 3 * q^91 - 3 * q^93

Decomposition of \(S_{1}^{\mathrm{new}}(111, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
111.1.h.a	$111$	$1$	111.h	111.h	$6$	$2$	$1$	$0.055$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	111.1.h.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)