Space of modular forms of level 112, weight 2, and Character 112.f

• Label: 112.2.f
• Level: $112$
• Weight: $2$
• Character orbit: 112.f
• Rep. character: $\chi_{112}(111,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(32\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(112, [\chi])\).

	Total	New	Old
Modular forms	22	4	18
Cusp forms	10	4	6
Eisenstein series	12	0	12

Trace form

\( 4 q + 4 q^{9} - 16 q^{21} - 28 q^{25} + 24 q^{29} - 8 q^{37} + 4 q^{49} + 24 q^{53} + 16 q^{57} + 48 q^{65} - 24 q^{77} - 44 q^{81} - 64 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(112, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.2.f.a	$112$	$2$	112.f	28.d	$2$	$2$	$2$	$0.894$	\(\Q(\sqrt{-3}) \)	None		✓			112.2.f.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 q^{3}-2\beta q^{5}+(-\beta+2)q^{7}+q^{9}+\cdots\)
112.2.f.b	$112$	$2$	112.f	28.d	$2$	$2$	$2$	$0.894$	\(\Q(\sqrt{-3}) \)	None		✓			112.2.f.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{3}+2\beta q^{5}+(-\beta-2)q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

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