Space of modular forms of level 112, weight 2, and Character 112.w

• Label: 112.2.w
• Level: $112$
• Weight: $2$
• Character orbit: 112.w
• Rep. character: $\chi_{112}(37,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $56$
• Newform subspaces: $3$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.w (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(32\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(112, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	56	56	0
Eisenstein series	16	16	0

Trace form

\( 56 q - 2 q^{2} - 2 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} - 20 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(112, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.2.w.a	$112$	$2$	112.w	112.w	$12$	$4$	$1$	$0.894$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(-4\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots\)
112.2.w.b	$112$	$2$	112.w	112.w	$12$	$4$	$1$	$0.894$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(4\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
112.2.w.c	$112$	$2$	112.w	112.w	$12$	$48$	$12$	$0.894$		None		$4$	$0$	\(-4\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$