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

• Label: 112.5.d
• Level: $112$
• Weight: $5$
• Character orbit: 112.d
• Rep. character: $\chi_{112}(15,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	112.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	70	12	58
Cusp forms	58	12	46
Eisenstein series	12	0	12

Trace form

12 * q - 72 * q^5 + 12 * q^9 - 360 * q^13 + 504 * q^17 + 996 * q^25 + 2520 * q^29 - 2592 * q^33 - 4200 * q^37 - 4392 * q^41 + 5592 * q^45 - 4116 * q^49 + 2520 * q^53 + 20736 * q^57 - 6600 * q^61 - 6480 * q^65 - 9120 * q^69 + 6264 * q^73 + 2124 * q^81 - 2256 * q^85 - 18504 * q^89 + 18240 * q^93 - 2952 * 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.d.a	$112$	$5$	112.d	4.b	$2$	$4$	$4$	$11.577$	\(\Q(\sqrt{-7}, \sqrt{13})\)	None		✓			112.5.d.a	$2$	$0$	\(0\)	\(0\)	\(-36\)	\(0\)	$2^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-9+\beta _{3})q^{5}-\beta _{2}q^{7}+(-17+\cdots)q^{9}+\cdots\)
112.5.d.b	$112$	$5$	112.d	4.b	$2$	$8$	$8$	$11.577$	8.0.\(\cdots\).1	None		✓	✓		112.5.d.b	$2$	$0$	\(0\)	\(0\)	\(-36\)	\(0\)	$2^{18}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-5-\beta _{3})q^{5}-\beta _{5}q^{7}+(9+\cdots)q^{9}+\cdots\)

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

\( S_{5}^{\mathrm{old}}(112, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)