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

• Label: 112.2.i
• Level: $112$
• Weight: $2$
• Character orbit: 112.i
• Rep. character: $\chi_{112}(65,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $32$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
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	44	10	34
Cusp forms	20	6	14
Eisenstein series	24	4	20

Trace form

6 * q + 3 * q^3 - q^5 + 4 * q^7 - 2 * q^9 - q^11 - 4 * q^13 - 2 * q^15 - q^17 + 5 * q^19 - 3 * q^21 - 7 * q^23 + 4 * q^25 - 18 * q^27 - 20 * q^29 - 13 * q^31 + 9 * q^33 - 21 * q^35 + 3 * q^37 + 14 * q^39 - 12 * q^41 + 24 * q^43 + 10 * q^45 - 3 * q^47 + 6 * q^49 + 17 * q^51 + 7 * q^53 + 22 * q^55 + 26 * q^57 + 27 * q^59 + 3 * q^61 + 38 * q^63 - 10 * q^65 - 5 * q^67 + 2 * q^69 - 32 * q^71 - 13 * q^73 - 4 * q^75 + 17 * q^77 - 23 * q^79 - 11 * q^81 - 40 * q^83 + 22 * q^85 - 26 * q^87 - 13 * q^89 - 24 * q^91 + 5 * q^93 - 9 * q^95 - 12 * q^97 + 12 * q^99

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.i.a	$112$	$2$	112.i	7.c	$3$	$2$	$1$	$0.894$	\(\Q(\sqrt{-3}) \)	None					56.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
112.2.i.b	$112$	$2$	112.i	7.c	$3$	$2$	$1$	$0.894$	\(\Q(\sqrt{-3}) \)	None					28.2.e.a	$2$	$0$	\(0\)	\(1\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
112.2.i.c	$112$	$2$	112.i	7.c	$3$	$2$	$1$	$0.894$	\(\Q(\sqrt{-3}) \)	None					56.2.i.a	$2$	$0$	\(0\)	\(3\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)

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

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