Space of modular forms of level 1488, weight 2, and Character 1488.q

• Label: 1488.2.q
• Level: $1488$
• Weight: $2$
• Character orbit: 1488.q
• Rep. character: $\chi_{1488}(625,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $15$
• Sturm bound: $512$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1488 = 2^{4} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1488.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(512\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1488, [\chi])\).

	Total	New	Old
Modular forms	536	64	472
Cusp forms	488	64	424
Eisenstein series	48	0	48

Trace form

64 * q - 2 * q^3 - 4 * q^7 - 32 * q^9 - 8 * q^15 - 2 * q^19 - 24 * q^25 + 4 * q^27 - 4 * q^31 + 8 * q^33 - 24 * q^35 - 4 * q^39 - 10 * q^43 - 48 * q^47 - 44 * q^49 - 4 * q^51 - 8 * q^53 + 16 * q^55 + 4 * q^57 - 40 * q^59 + 8 * q^63 + 8 * q^67 - 16 * q^69 + 32 * q^71 + 12 * q^73 - 14 * q^75 + 16 * q^77 - 32 * q^81 - 20 * q^83 - 48 * q^85 + 16 * q^89 - 48 * q^91 + 8 * q^93 - 32 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1488, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1488.2.q.a	$1488$	$2$	1488.q	31.c	$3$	$2$	$1$	$11.882$	\(\Q(\sqrt{-3}) \)	None					744.2.q.c	$2$	$1$	\(0\)	\(-1\)	\(-2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{7}+\cdots\)
1488.2.q.b	$1488$	$2$	1488.q	31.c	$3$	$2$	$1$	$11.882$	\(\Q(\sqrt{-3}) \)	None					186.2.e.a	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
1488.2.q.c	$1488$	$2$	1488.q	31.c	$3$	$2$	$1$	$11.882$	\(\Q(\sqrt{-3}) \)	None					744.2.q.a	$2$	$0$	\(0\)	\(1\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}-2\zeta_{6}q^{11}+\cdots\)
1488.2.q.d	$1488$	$2$	1488.q	31.c	$3$	$2$	$1$	$11.882$	\(\Q(\sqrt{-3}) \)	None					744.2.q.b	$2$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}-4\zeta_{6}q^{11}+\cdots\)
1488.2.q.e	$1488$	$2$	1488.q	31.c	$3$	$2$	$1$	$11.882$	\(\Q(\sqrt{-3}) \)	None					186.2.e.b	$2$	$0$	\(0\)	\(1\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1488.2.q.f	$1488$	$2$	1488.q	31.c	$3$	$4$	$2$	$11.882$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					186.2.e.d	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{3}+2\beta _{1}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots\)
1488.2.q.g	$1488$	$2$	1488.q	31.c	$3$	$4$	$2$	$11.882$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					93.2.e.a	$2$	$0$	\(0\)	\(-2\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
1488.2.q.h	$1488$	$2$	1488.q	31.c	$3$	$4$	$2$	$11.882$	\(\Q(\sqrt{-3}, \sqrt{19})\)	None					186.2.e.c	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{3}+\beta _{1}q^{7}+\beta _{2}q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
1488.2.q.i	$1488$	$2$	1488.q	31.c	$3$	$4$	$2$	$11.882$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None					372.2.i.a	$2$	$0$	\(0\)	\(2\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+2\beta _{2}q^{7}+\cdots\)
1488.2.q.j	$1488$	$2$	1488.q	31.c	$3$	$4$	$2$	$11.882$	\(\Q(\sqrt{-3}, \sqrt{41})\)	None					744.2.q.d	$2$	$0$	\(0\)	\(2\)	\(4\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{3}+(2-2\beta _{2})q^{5}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
1488.2.q.k	$1488$	$2$	1488.q	31.c	$3$	$6$	$3$	$11.882$	6.0.65370672.1	None					372.2.i.b	$2$	$0$	\(0\)	\(-3\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{3}+(-1-\beta _{1}+\beta _{2}-\beta _{4})q^{5}+\cdots\)
1488.2.q.l	$1488$	$2$	1488.q	31.c	$3$	$6$	$3$	$11.882$	6.0.591408.1	None					744.2.q.f	$2$	$0$	\(0\)	\(-3\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{4})q^{3}+(\beta _{1}+\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
1488.2.q.m	$1488$	$2$	1488.q	31.c	$3$	$6$	$3$	$11.882$	6.0.591408.1	None					93.2.e.b	$2$	$0$	\(0\)	\(3\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{4})q^{3}+(2\beta _{1}-\beta _{3}-2\beta _{4}+\beta _{5})q^{5}+\cdots\)
1488.2.q.n	$1488$	$2$	1488.q	31.c	$3$	$6$	$3$	$11.882$	6.0.349142832.2	None					744.2.q.e	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{3}-\beta _{1}q^{7}+(-1+\beta _{3})q^{9}+(2+\cdots)q^{11}+\cdots\)
1488.2.q.o	$1488$	$2$	1488.q	31.c	$3$	$10$	$5$	$11.882$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None			✓		744.2.q.g	$2$	$0$	\(0\)	\(-5\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{3}+\beta _{2}q^{5}-\beta _{6}q^{7}+(-1+\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1488, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1488, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(124, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(248, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(372, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(496, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(744, [\chi])\)\(^{\oplus 2}\)