Space of modular forms of level 888, weight 2, and Character 888.q

• Label: 888.2.q
• Level: $888$
• Weight: $2$
• Character orbit: 888.q
• Rep. character: $\chi_{888}(121,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $9$
• Sturm bound: $304$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(304\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(888, [\chi])\).

	Total	New	Old
Modular forms	320	40	280
Cusp forms	288	40	248
Eisenstein series	32	0	32

Trace form

40 * q + 2 * q^3 - 2 * q^5 - 2 * q^7 - 20 * q^9 - 8 * q^11 + 2 * q^13 - 2 * q^17 + 8 * q^19 - 6 * q^21 - 22 * q^25 - 4 * q^27 - 4 * q^29 + 20 * q^31 - 4 * q^33 + 2 * q^37 + 2 * q^39 + 22 * q^41 - 12 * q^43 + 4 * q^45 - 16 * q^47 - 2 * q^49 - 16 * q^53 - 12 * q^55 + 8 * q^57 + 4 * q^59 + 6 * q^61 + 4 * q^63 - 8 * q^65 + 14 * q^67 + 4 * q^69 + 4 * q^71 + 20 * q^73 - 28 * q^75 + 8 * q^77 - 10 * q^79 - 20 * q^81 + 36 * q^83 + 60 * q^85 - 8 * q^87 - 18 * q^89 - 2 * q^91 - 14 * q^93 - 8 * q^95 + 24 * q^97 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(888, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
888.2.q.a	$888$	$2$	888.q	37.c	$3$	$2$	$1$	$7.091$	\(\Q(\sqrt{-3}) \)	None		✓			888.2.q.a	$2$	$1$	\(0\)	\(-1\)	\(2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}+2\zeta_{6}q^{5}-3\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots\)
888.2.q.b	$888$	$2$	888.q	37.c	$3$	$2$	$1$	$7.091$	\(\Q(\sqrt{-3}) \)	None		✓			888.2.q.b	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}+2\zeta_{6}q^{5}-3\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots\)
888.2.q.c	$888$	$2$	888.q	37.c	$3$	$2$	$1$	$7.091$	\(\Q(\sqrt{-3}) \)	None		✓			888.2.q.c	$2$	$1$	\(0\)	\(1\)	\(-4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{7}+(-1+\zeta_{6})q^{9}+\cdots\)
888.2.q.d	$888$	$2$	888.q	37.c	$3$	$2$	$1$	$7.091$	\(\Q(\sqrt{-3}) \)	None		✓			888.2.q.d	$2$	$0$	\(0\)	\(1\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{3}+\zeta_{6}q^{5}+4\zeta_{6}q^{7}+(-1+\zeta_{6})q^{9}+\cdots\)
888.2.q.e	$888$	$2$	888.q	37.c	$3$	$6$	$3$	$7.091$	6.0.1415907.1	None		✓			888.2.q.e	$2$	$0$	\(0\)	\(-3\)	\(-6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{4})q^{3}+(-2+\beta _{1}-2\beta _{4}+\cdots)q^{5}+\cdots\)
888.2.q.f	$888$	$2$	888.q	37.c	$3$	$6$	$3$	$7.091$	6.0.1415907.1	None		✓			888.2.q.f	$2$	$0$	\(0\)	\(3\)	\(-2\)	\(-7\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3}-\beta _{4})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
888.2.q.g	$888$	$2$	888.q	37.c	$3$	$6$	$3$	$7.091$	6.0.47545083.2	None		✓			888.2.q.g	$2$	$0$	\(0\)	\(3\)	\(1\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{3}-\beta _{5}q^{5}-3\beta _{4}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
888.2.q.h	$888$	$2$	888.q	37.c	$3$	$6$	$3$	$7.091$	6.0.50898483.1	None		✓			888.2.q.h	$2$	$0$	\(0\)	\(3\)	\(3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{3})q^{5}-\beta _{3}q^{7}+\cdots\)
888.2.q.i	$888$	$2$	888.q	37.c	$3$	$8$	$4$	$7.091$	8.0.1445900625.1	None		✓	✓		888.2.q.i	$2$	$0$	\(0\)	\(-4\)	\(1\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{3})q^{3}+(-\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(888, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(888, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 2}\)