Space of modular forms of level 112, weight 4, and Character 112.i

• Label: 112.4.i
• Level: $112$
• Weight: $4$
• Character orbit: 112.i
• Rep. character: $\chi_{112}(65,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $22$
• Newform subspaces: $6$
• Sturm bound: $64$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	112.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(64\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(112, [\chi])\).

	Total	New	Old
Modular forms	108	26	82
Cusp forms	84	22	62
Eisenstein series	24	4	20

Trace form

22 * q - 5 * q^3 - q^5 + 20 * q^7 - 82 * q^9 - 9 * q^11 - 4 * q^13 - 50 * q^15 - q^17 - 203 * q^19 + 93 * q^21 - 39 * q^23 - 260 * q^25 + 382 * q^27 + 140 * q^29 + 307 * q^31 + 65 * q^33 - 357 * q^35 - 5 * q^37 - 458 * q^39 + 292 * q^41 + 744 * q^43 + 442 * q^45 + 573 * q^47 - 490 * q^49 - 247 * q^51 - 9 * q^53 - 58 * q^55 - 966 * q^57 - 1405 * q^59 - 101 * q^61 - 546 * q^63 + 246 * q^65 + 595 * q^67 + 3122 * q^69 - 896 * q^71 - 1093 * q^73 - 780 * q^75 - 407 * q^77 + 1033 * q^79 - 115 * q^81 + 3848 * q^83 - 1050 * q^85 + 2350 * q^87 - 645 * q^89 + 3240 * q^91 + 565 * q^93 - 1113 * q^95 - 2332 * q^97 - 5636 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(112, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.4.i.a	$112$	$4$	112.i	7.c	$3$	$2$	$1$	$6.608$	\(\Q(\sqrt{-3}) \)	None					14.4.c.a	$2$	$0$	\(0\)	\(-5\)	\(9\)	\(28\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-5+5\zeta_{6})q^{3}+9\zeta_{6}q^{5}+(21-14\zeta_{6})q^{7}+\cdots\)
112.4.i.b	$112$	$4$	112.i	7.c	$3$	$2$	$1$	$6.608$	\(\Q(\sqrt{-3}) \)	None					14.4.c.b	$2$	$0$	\(0\)	\(-1\)	\(-7\)	\(20\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-7\zeta_{6}q^{5}+(1+18\zeta_{6})q^{7}+\cdots\)
112.4.i.c	$112$	$4$	112.i	7.c	$3$	$2$	$1$	$6.608$	\(\Q(\sqrt{-3}) \)	None					7.4.c.a	$2$	$0$	\(0\)	\(7\)	\(-7\)	\(-28\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(7-7\zeta_{6})q^{3}-7\zeta_{6}q^{5}+(-7-14\zeta_{6})q^{7}+\cdots\)
112.4.i.d	$112$	$4$	112.i	7.c	$3$	$4$	$2$	$6.608$	\(\Q(\sqrt{-3}, \sqrt{37})\)	None					28.4.e.a	$2$	$0$	\(0\)	\(0\)	\(14\)	\(-24\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(7-7\beta _{1}+2\beta _{2}+2\beta _{3})q^{5}+\cdots\)
112.4.i.e	$112$	$4$	112.i	7.c	$3$	$6$	$3$	$6.608$	6.0.11163123.4	None					56.4.i.b	$2$	$0$	\(0\)	\(-7\)	\(3\)	\(4\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2\beta _{1}+\beta _{5})q^{3}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
112.4.i.f	$112$	$4$	112.i	7.c	$3$	$6$	$3$	$6.608$	6.0.11163123.4	None					56.4.i.a	$2$	$0$	\(0\)	\(1\)	\(-13\)	\(20\)	$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{3}+(-5+5\beta _{1}-\beta _{3}-\beta _{4}-2\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(112, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)