Space of modular forms of level 112, weight 6, and Character 112.p

• Label: 112.6.p
• Level: $112$
• Weight: $6$
• Character orbit: 112.p
• Rep. character: $\chi_{112}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	112.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(112, [\chi])\).

	Total	New	Old
Modular forms	172	40	132
Cusp forms	148	40	108
Eisenstein series	24	0	24

Trace form

40 * q - 1620 * q^9 + 6708 * q^21 + 8408 * q^25 + 23880 * q^29 + 42444 * q^33 - 1076 * q^37 - 53100 * q^45 - 73184 * q^49 + 26268 * q^53 + 111000 * q^57 - 56556 * q^61 - 27324 * q^65 + 78852 * q^73 + 198672 * q^77 - 384216 * q^81 - 282792 * q^85 + 14220 * q^89 + 312564 * q^93

Decomposition of \(S_{6}^{\mathrm{new}}(112, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.6.p.a	$112$	$6$	112.p	28.f	$6$	$12$	$6$	$17.963$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			112.6.p.a	$4$	$0$	\(0\)	\(0\)	\(-66\)	\(0\)	$2^{16}\cdot 3^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{3}+(-7+4\beta _{2}+\beta _{9})q^{5}+(-2\beta _{3}+\cdots)q^{7}+\cdots\)
112.6.p.b	$112$	$6$	112.p	28.f	$6$	$14$	$7$	$17.963$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			112.6.p.b	$2$	$0$	\(0\)	\(-9\)	\(33\)	\(-28\)	$2^{20}\cdot 3^{6}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{1}-\beta _{5})q^{3}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
112.6.p.c	$112$	$6$	112.p	28.f	$6$	$14$	$7$	$17.963$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			112.6.p.b	$2$	$0$	\(0\)	\(9\)	\(33\)	\(28\)	$2^{20}\cdot 3^{6}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{1}+\beta _{5})q^{3}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(112, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)