Space of modular forms of level 112, weight 8, and Character 112.i

• Label: 112.8.i
• Level: $112$
• Weight: $8$
• Character orbit: 112.i
• Rep. character: $\chi_{112}(65,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $54$
• Newform subspaces: $6$
• Sturm bound: $128$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(128\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(112, [\chi])\).

	Total	New	Old
Modular forms	236	58	178
Cusp forms	212	54	158
Eisenstein series	24	4	20

Trace form

54 * q - 53 * q^3 - q^5 - 1004 * q^7 - 18226 * q^9 - 601 * q^11 - 4 * q^13 - 4370 * q^15 - q^17 - 50731 * q^19 + 3357 * q^21 - 43783 * q^23 - 369620 * q^25 + 310558 * q^27 - 76340 * q^29 - 36301 * q^31 + 132785 * q^33 + 43323 * q^35 + 207787 * q^37 + 98086 * q^39 + 254340 * q^41 + 375304 * q^43 - 350438 * q^45 + 1302333 * q^47 + 1293494 * q^49 + 1559801 * q^51 - 796457 * q^53 - 6048538 * q^55 - 231942 * q^57 - 3237837 * q^59 + 912523 * q^61 + 2139630 * q^63 - 2144074 * q^65 - 5616221 * q^67 - 3737326 * q^69 + 6480448 * q^71 + 4281803 * q^73 - 14189340 * q^75 + 5769305 * q^77 - 5604311 * q^79 - 11419267 * q^81 + 20441192 * q^83 - 7003130 * q^85 + 8608798 * q^87 + 5740043 * q^89 - 28818968 * q^91 + 1821973 * q^93 - 10921113 * q^95 + 9642180 * q^97 + 69720604 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(112, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.8.i.a	$112$	$8$	112.i	7.c	$3$	$4$	$2$	$34.987$	\(\Q(\sqrt{-3}, \sqrt{2389})\)	None					14.8.c.a	$2$	$0$	\(0\)	\(-56\)	\(238\)	\(-168\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-28\beta _{1}-\beta _{2})q^{3}+(119-119\beta _{1}+\cdots)q^{5}+\cdots\)
112.8.i.b	$112$	$8$	112.i	7.c	$3$	$4$	$2$	$34.987$	\(\Q(\sqrt{-3}, \sqrt{949})\)	None					14.8.c.b	$2$	$0$	\(0\)	\(56\)	\(14\)	\(1848\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(28\beta _{1}+\beta _{2})q^{3}+(7-7\beta _{1}+14\beta _{2}+\cdots)q^{5}+\cdots\)
112.8.i.c	$112$	$8$	112.i	7.c	$3$	$8$	$4$	$34.987$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					7.8.c.a	$2$	$0$	\(0\)	\(28\)	\(-252\)	\(-672\)	$2^{14}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(7-7\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(-63\beta _{1}+\cdots)q^{5}+\cdots\)
112.8.i.d	$112$	$8$	112.i	7.c	$3$	$10$	$5$	$34.987$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					28.8.e.a	$2$	$0$	\(0\)	\(-27\)	\(249\)	\(-332\)	$2^{18}\cdot 3^{4}\cdot 7^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-5+5\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(7^{2}\beta _{1}+\cdots)q^{5}+\cdots\)
112.8.i.e	$112$	$8$	112.i	7.c	$3$	$14$	$7$	$34.987$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					56.8.i.b	$2$	$0$	\(0\)	\(-29\)	\(-237\)	\(-724\)	$2^{36}\cdot 3^{2}\cdot 7^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4-\beta _{1}-\beta _{2}-4\beta _{3})q^{3}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
112.8.i.f	$112$	$8$	112.i	7.c	$3$	$14$	$7$	$34.987$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					56.8.i.a	$2$	$0$	\(0\)	\(-25\)	\(-13\)	\(-956\)	$2^{36}\cdot 3^{2}\cdot 7^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+\beta _{1}+4\beta _{3}+\beta _{4})q^{3}+(-2\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(112, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)