Space of modular forms of level 112, weight 4, and Character 112.p

• Label: 112.4.p
• Level: $112$
• Weight: $4$
• Character orbit: 112.p
• Rep. character: $\chi_{112}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $7$
• Sturm bound: $64$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	112.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(64\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(112, [\chi])\).

	Total	New	Old
Modular forms	108	24	84
Cusp forms	84	24	60
Eisenstein series	24	0	24

Trace form

\( 24 q - 108 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(112, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.4.p.a	$112$	$4$	112.p	28.f	$6$	$2$	$1$	$6.608$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-7\)	\(27\)	\(28\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-7+7\zeta_{6})q^{3}+(18-9\zeta_{6})q^{5}+(7+\cdots)q^{7}+\cdots\)
112.4.p.b	$112$	$4$	112.p	28.f	$6$	$2$	$1$	$6.608$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-9\)	\(28\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(-6+3\zeta_{6})q^{5}+(21+\cdots)q^{7}+\cdots\)
112.4.p.c	$112$	$4$	112.p	28.f	$6$	$2$	$1$	$6.608$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-9\)	\(-28\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(-6+3\zeta_{6})q^{5}+(-21+\cdots)q^{7}+\cdots\)
112.4.p.d	$112$	$4$	112.p	28.f	$6$	$2$	$1$	$6.608$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(7\)	\(27\)	\(-28\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(7-7\zeta_{6})q^{3}+(18-9\zeta_{6})q^{5}+(-7+\cdots)q^{7}+\cdots\)
112.4.p.e	$112$	$4$	112.p	28.f	$6$	$4$	$2$	$6.608$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(-30\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}+(-10-5\beta _{2})q^{5}+(-8\beta _{1}+\cdots)q^{7}+\cdots\)
112.4.p.f	$112$	$4$	112.p	28.f	$6$	$6$	$3$	$6.608$	6.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(-7\)	\(-3\)	\(52\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2\beta _{3}+\beta _{5})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(4+\cdots)q^{7}+\cdots\)
112.4.p.g	$112$	$4$	112.p	28.f	$6$	$6$	$3$	$6.608$	6.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(7\)	\(-3\)	\(-52\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2\beta _{3}-\beta _{5})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

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