Space of modular forms of level 112, weight 3, and Character 112.d

• Label: 112.3.d
• Level: $112$
• Weight: $3$
• Character orbit: 112.d
• Rep. character: $\chi_{112}(15,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(112, [\chi])\).

	Total	New	Old
Modular forms	38	6	32
Cusp forms	26	6	20
Eisenstein series	12	0	12

Trace form

\( 6 q + 12 q^{5} - 42 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(112, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.3.d.a	$112$	$3$	112.d	4.b	$2$	$2$	$2$	$3.052$	\(\Q(\sqrt{-7}) \)	None		$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta q^{3}+8q^{5}+\beta q^{7}-19q^{9}-4\beta q^{11}+\cdots\)
112.3.d.b	$112$	$3$	112.d	4.b	$2$	$4$	$4$	$3.052$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(112, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)