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

• Label: 112.10.f
• Level: $112$
• Weight: $10$
• Character orbit: 112.f
• Rep. character: $\chi_{112}(111,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	112.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(160\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	150	36	114
Cusp forms	138	36	102
Eisenstein series	12	0	12

Trace form

\( 36 q + 236196 q^{9} + O(q^{10}) \)

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.f.a	$112$	$10$	112.f	28.d	$2$	$12$	$12$	$57.684$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{38}\cdot 3^{4}\cdot 7^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{3}q^{5}+(\beta _{4}-\beta _{5})q^{7}+(6702+\cdots)q^{9}+\cdots\)
112.10.f.b	$112$	$10$	112.f	28.d	$2$	$24$	$24$	$57.684$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{10}^{\mathrm{old}}(112, [\chi]) \cong \)