Space of modular forms of level 112, weight 12, and Character 112.i

• Label: 112.12.i
• Level: $112$
• Weight: $12$
• Character orbit: 112.i
• Rep. character: $\chi_{112}(65,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $86$
• Newform subspaces: $6$
• Sturm bound: $192$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
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:			\(192\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(112, [\chi])\).

	Total	New	Old
Modular forms	364	90	274
Cusp forms	340	86	254
Eisenstein series	24	4	20

Trace form

86 * q - 485 * q^3 - q^5 + 51348 * q^7 - 2421010 * q^9 + 270423 * q^11 - 4 * q^13 - 354290 * q^15 - q^17 - 2687115 * q^19 - 12388899 * q^21 - 2540391 * q^23 - 356918180 * q^25 + 229228222 * q^27 + 115307276 * q^29 + 19233075 * q^31 - 177987295 * q^33 - 578735397 * q^35 - 261381029 * q^37 + 999395734 * q^39 - 144100892 * q^41 - 3208821976 * q^43 + 1188116602 * q^45 + 866611773 * q^47 - 1652994730 * q^49 - 1241224471 * q^51 + 957403575 * q^53 - 2114024698 * q^55 + 70037946 * q^57 - 7120442269 * q^59 + 1342607995 * q^61 + 7101432702 * q^63 - 7816060554 * q^65 - 10713704333 * q^67 + 4702354418 * q^69 - 33364113920 * q^71 - 3676801573 * q^73 - 7231757100 * q^75 + 49535925577 * q^77 - 21202067255 * q^79 - 84373142419 * q^81 + 65567040968 * q^83 - 26081115610 * q^85 - 6482482802 * q^87 - 86435661669 * q^89 - 11134198744 * q^91 - 117661469195 * q^93 + 187037298087 * q^95 - 175876564316 * q^97 - 415747420868 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(112, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.12.i.a	$112$	$12$	112.i	7.c	$3$	$8$	$4$	$86.054$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					14.12.c.a	$2$	$0$	\(0\)	\(-266\)	\(7504\)	\(42224\)	$2^{12}\cdot 3\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-67+\beta _{1}+67\beta _{2})q^{3}+(1876\beta _{2}+\cdots)q^{5}+\cdots\)
112.12.i.b	$112$	$12$	112.i	7.c	$3$	$8$	$4$	$86.054$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					14.12.c.b	$2$	$0$	\(0\)	\(266\)	\(3808\)	\(-110328\)	$2^{12}\cdot 3\cdot 7^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(67-\beta _{1}-67\beta _{2})q^{3}+(952\beta _{2}-\beta _{5}+\cdots)q^{5}+\cdots\)
112.12.i.c	$112$	$12$	112.i	7.c	$3$	$12$	$6$	$86.054$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					7.12.c.a	$2$	$0$	\(0\)	\(244\)	\(-8782\)	\(504\)	$2^{32}\cdot 3^{3}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-41\beta _{1}-\beta _{5})q^{3}+(-1463-1463\beta _{1}+\cdots)q^{5}+\cdots\)
112.12.i.d	$112$	$12$	112.i	7.c	$3$	$14$	$7$	$86.054$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					28.12.e.a	$2$	$0$	\(0\)	\(-243\)	\(3719\)	\(83356\)	$2^{42}\cdot 3^{5}\cdot 7^{11}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-35\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(531-531\beta _{1}+\cdots)q^{5}+\cdots\)
112.12.i.e	$112$	$12$	112.i	7.c	$3$	$22$	$11$	$86.054$		None					56.12.i.b	$2$	$0$	\(0\)	\(-463\)	\(-1277\)	\(20812\)		$\mathrm{SU}(2)[C_{3}]$
112.12.i.f	$112$	$12$	112.i	7.c	$3$	$22$	$11$	$86.054$		None					56.12.i.a	$2$	$0$	\(0\)	\(-23\)	\(-4973\)	\(14780\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{12}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(112, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)