Space of modular forms of level 576, weight 3, and Character 576.q

• Label: 576.3.q
• Level: $576$
• Weight: $3$
• Character orbit: 576.q
• Rep. character: $\chi_{576}(65,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $12$
• Sturm bound: $288$
• Trace bound: $9$

Defining parameters

Level:	$N$	$=$	$576 = 2^{6} \cdot 3^{2}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	576.q (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$9$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$12$
Sturm bound:			$288$
Trace bound:			$9$
Distinguishing $T_p$:			$5$, $7$

Dimensions

The following table gives the dimensions of various subspaces of $M_{3}(576, [\chi])$.

	Total	New	Old
Modular forms	408	100	308
Cusp forms	360	92	268
Eisenstein series	48	8	40

Trace form

92 * q + 6 * q^5 - 4 * q^9 + 2 * q^13 - 14 * q^21 + 188 * q^25 + 6 * q^29 - 54 * q^33 + 8 * q^37 + 138 * q^41 + 6 * q^45 - 240 * q^49 - 120 * q^57 + 2 * q^61 - 6 * q^65 + 262 * q^69 - 8 * q^73 + 6 * q^77 + 140 * q^81 - 48 * q^85 + 706 * q^93 - 2 * q^97

Decomposition of $S_{3}^{\mathrm{new}}(576, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
576.3.q.a	$576$	$3$	576.q	9.d	$6$	$2$	$1$	$15.695$	$\Q(\sqrt{-3})$	None					9.3.d.a	$2$	$0$	$0$	$-3$	$-6$	$2$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-3+3\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+\cdots$
576.3.q.b	$576$	$3$	576.q	9.d	$6$	$2$	$1$	$15.695$	$\Q(\sqrt{-3})$	None					9.3.d.a	$2$	$0$	$0$	$3$	$-6$	$-2$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(3-3\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots$
576.3.q.c	$576$	$3$	576.q	9.d	$6$	$4$	$2$	$15.695$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					72.3.m.a	$2$	$0$	$0$	$-12$	$-6$	$6$	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-3q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots$
576.3.q.d	$576$	$3$	576.q	9.d	$6$	$4$	$2$	$15.695$	$\Q(\sqrt{-3}, \sqrt{-11})$	None					36.3.g.a	$2$	$0$	$0$	$-3$	$-9$	$-1$	$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{3})q^{3}+(-4+\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots$
576.3.q.e	$576$	$3$	576.q	9.d	$6$	$4$	$2$	$15.695$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					18.3.d.a	$2$	$0$	$0$	$0$	$18$	$-2$	$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\beta _{1}+\beta _{3})q^{3}+(3+3\beta _{1})q^{5}+\cdots$
576.3.q.f	$576$	$3$	576.q	9.d	$6$	$4$	$2$	$15.695$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					18.3.d.a	$2$	$0$	$0$	$0$	$18$	$2$	$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-2\beta _{1}+\beta _{3})q^{3}+(3+3\beta _{1})q^{5}+\cdots$
576.3.q.g	$576$	$3$	576.q	9.d	$6$	$4$	$2$	$15.695$	$\Q(\sqrt{-3}, \sqrt{-11})$	None					36.3.g.a	$2$	$0$	$0$	$3$	$-9$	$1$	$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{3})q^{3}+(-4+\beta _{1}-2\beta _{2}+\beta _{3})q^{5}+\cdots$
576.3.q.h	$576$	$3$	576.q	9.d	$6$	$4$	$2$	$15.695$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					72.3.m.a	$2$	$0$	$0$	$12$	$-6$	$-6$	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+3q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
576.3.q.i	$576$	$3$	576.q	9.d	$6$	$8$	$4$	$15.695$	8.0.$\cdots$.9	None					72.3.m.b	$2$	$0$	$0$	$-10$	$6$	$6$	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{2}+\beta _{7})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
576.3.q.j	$576$	$3$	576.q	9.d	$6$	$8$	$4$	$15.695$	8.0.$\cdots$.9	None					72.3.m.b	$2$	$0$	$0$	$10$	$6$	$-6$	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{2}-\beta _{7})q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots$
576.3.q.k	$576$	$3$	576.q	9.d	$6$	$24$	$12$	$15.695$		None					288.3.q.a	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$
576.3.q.l	$576$	$3$	576.q	9.d	$6$	$24$	$12$	$15.695$		None					288.3.q.b	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$

Decomposition of $S_{3}^{\mathrm{old}}(576, [\chi])$ into lower level spaces

$S_{3}^{\mathrm{old}}(576, [\chi]) \simeq$ $S_{3}^{\mathrm{new}}(9, [\chi])$$^{\oplus 7}$$\oplus$$S_{3}^{\mathrm{new}}(18, [\chi])$$^{\oplus 6}$$\oplus$$S_{3}^{\mathrm{new}}(36, [\chi])$$^{\oplus 5}$$\oplus$$S_{3}^{\mathrm{new}}(72, [\chi])$$^{\oplus 4}$$\oplus$$S_{3}^{\mathrm{new}}(144, [\chi])$$^{\oplus 3}$$\oplus$$S_{3}^{\mathrm{new}}(288, [\chi])$$^{\oplus 2}$