Space of modular forms of level 112, weight 10, and Character 112.p

• Label: 112.10.p
• Level: $112$
• Weight: $10$
• Character orbit: 112.p
• Rep. character: $\chi_{112}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $160$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(160\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(112, [\chi])\).

	Total	New	Old
Modular forms	300	72	228
Cusp forms	276	72	204
Eisenstein series	24	0	24

Trace form

\( 72 q - 236196 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(112, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.10.p.a	$112$	$10$	112.p	28.f	$6$	$24$	$12$	$57.684$		None		$2$	$0$	\(0\)	\(-162\)	\(-852\)	\(-6744\)		$\mathrm{SU}(2)[C_{6}]$
112.10.p.b	$112$	$10$	112.p	28.f	$6$	$24$	$12$	$57.684$		None		$4$	$0$	\(0\)	\(0\)	\(1704\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
112.10.p.c	$112$	$10$	112.p	28.f	$6$	$24$	$12$	$57.684$		None		$2$	$0$	\(0\)	\(162\)	\(-852\)	\(6744\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{10}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(112, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)