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

• Label: 112.4.i
• Level: $112$
• Weight: $4$
• Character orbit: 112.i
• Rep. character: $\chi_{112}(65,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $22$
• Newform subspaces: $6$
• Sturm bound: $64$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	112.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
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	26	82
Cusp forms	84	22	62
Eisenstein series	24	4	20

Trace form

\( 22 q - 5 q^{3} - q^{5} + 20 q^{7} - 82 q^{9} + O(q^{10}) \)

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.i.a	$112$	$4$	112.i	7.c	$3$	$2$	$1$	$6.608$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-5\)	\(9\)	\(28\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-5+5\zeta_{6})q^{3}+9\zeta_{6}q^{5}+(21-14\zeta_{6})q^{7}+\cdots\)
112.4.i.b	$112$	$4$	112.i	7.c	$3$	$2$	$1$	$6.608$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-7\)	\(20\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-7\zeta_{6}q^{5}+(1+18\zeta_{6})q^{7}+\cdots\)
112.4.i.c	$112$	$4$	112.i	7.c	$3$	$2$	$1$	$6.608$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(7\)	\(-7\)	\(-28\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(7-7\zeta_{6})q^{3}-7\zeta_{6}q^{5}+(-7-14\zeta_{6})q^{7}+\cdots\)
112.4.i.d	$112$	$4$	112.i	7.c	$3$	$4$	$2$	$6.608$	\(\Q(\sqrt{-3}, \sqrt{37})\)	None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(-24\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(7-7\beta _{1}+2\beta _{2}+2\beta _{3})q^{5}+\cdots\)
112.4.i.e	$112$	$4$	112.i	7.c	$3$	$6$	$3$	$6.608$	6.0.11163123.4	None		$2$	$0$	\(0\)	\(-7\)	\(3\)	\(4\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2\beta _{1}+\beta _{5})q^{3}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
112.4.i.f	$112$	$4$	112.i	7.c	$3$	$6$	$3$	$6.608$	6.0.11163123.4	None		$2$	$0$	\(0\)	\(1\)	\(-13\)	\(20\)	$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{3}+(-5+5\beta _{1}-\beta _{3}-\beta _{4}-2\beta _{5})q^{5}+\cdots\)

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

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