Space of modular forms of level 112, weight 5, and Character 112.r

• Label: 112.5.r
• Level: $112$
• Weight: $5$
• Character orbit: 112.r
• Rep. character: $\chi_{112}(79,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $80$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	112.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(80\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(112, [\chi])\).

	Total	New	Old
Modular forms	140	32	108
Cusp forms	116	32	84
Eisenstein series	24	0	24

Trace form

32 * q + 432 * q^9 - 352 * q^13 - 1200 * q^21 - 3104 * q^25 + 3168 * q^29 + 2160 * q^33 - 1040 * q^37 + 3744 * q^41 - 1200 * q^45 + 9440 * q^49 + 2448 * q^53 - 14304 * q^57 - 14480 * q^61 - 17136 * q^65 + 26112 * q^69 + 14960 * q^73 - 44064 * q^77 - 576 * q^81 + 35232 * q^85 + 16272 * q^89 + 32304 * q^93 + 8672 * q^97

Decomposition of \(S_{5}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.5.r.a	$112$	$5$	112.r	28.g	$6$	$10$	$5$	$11.577$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓			112.5.r.a	$2$	$0$	\(0\)	\(-9\)	\(9\)	\(-10\)	$2^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{3}+\beta _{4})q^{3}+(2-2\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
112.5.r.b	$112$	$5$	112.r	28.g	$6$	$10$	$5$	$11.577$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓			112.5.r.a	$2$	$0$	\(0\)	\(9\)	\(9\)	\(10\)	$2^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{3}-\beta _{4})q^{3}+(2-2\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
112.5.r.c	$112$	$5$	112.r	28.g	$6$	$12$	$6$	$11.577$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		112.5.r.c	$4$	$0$	\(0\)	\(0\)	\(-18\)	\(0\)	$2^{14}\cdot 7^{5}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{3}+(-3+3\beta _{1}+\beta _{4}-\beta _{9})q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(112, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)