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

• Label: 112.3.c
• Level: $112$
• Weight: $3$
• Character orbit: 112.c
• Rep. character: $\chi_{112}(97,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
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	9	29
Cusp forms	26	7	19
Eisenstein series	12	2	10

Trace form

\( 7 q - 7 q^{7} - 17 q^{9} + O(q^{10}) \)

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.c.a	$112$	$3$	112.c	7.b	$2$	$1$	$1$	$3.052$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(7\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+7q^{7}+9q^{9}+6q^{11}-18q^{23}+5^{2}q^{25}+\cdots\)
112.3.c.b	$112$	$3$	112.c	7.b	$2$	$2$	$2$	$3.052$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+\beta q^{5}+(-5-\beta )q^{7}-15q^{9}+\cdots\)
112.3.c.c	$112$	$3$	112.c	7.b	$2$	$4$	$4$	$3.052$	4.0.2048.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(112, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)