Space of modular forms of level 1512, weight 2, and Character 1512.q

• Label: 1512.2.q
• Level: $1512$
• Weight: $2$
• Character orbit: 1512.q
• Rep. character: $\chi_{1512}(793,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $576$
• Trace bound: $5$

Defining parameters

Level:	$N$	$=$	$1512 = 2^{3} \cdot 3^{3} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1512.q (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$63$
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$4$
Sturm bound:			$576$
Trace bound:			$5$
Distinguishing $T_p$:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(1512, [\chi])$.

	Total	New	Old
Modular forms	624	48	576
Cusp forms	528	48	480
Eisenstein series	96	0	96

Trace form

48 * q - 4 * q^5 - 8 * q^17 + 4 * q^23 - 24 * q^25 + 6 * q^29 - 12 * q^31 - 12 * q^35 - 18 * q^41 + 6 * q^43 + 12 * q^47 - 6 * q^49 - 4 * q^53 + 12 * q^55 - 72 * q^59 - 12 * q^61 + 24 * q^65 + 40 * q^71 - 28 * q^77 + 12 * q^79 + 36 * q^83 - 18 * q^89 - 6 * q^91 - 20 * q^95

Decomposition of $S_{2}^{\mathrm{new}}(1512, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1512.2.q.a	$1512$	$2$	1512.q	63.h	$3$	$2$	$1$	$12.073$	$\Q(\sqrt{-3})$	None					504.2.q.b	$2$	$1$	$0$	$0$	$-1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots$
1512.2.q.b	$1512$	$2$	1512.q	63.h	$3$	$2$	$1$	$12.073$	$\Q(\sqrt{-3})$	None					504.2.q.a	$2$	$0$	$0$	$0$	$1$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots$
1512.2.q.c	$1512$	$2$	1512.q	63.h	$3$	$22$	$11$	$12.073$		None					504.2.q.d	$2$	$0$	$0$	$0$	$-3$	$-5$		$\mathrm{SU}(2)[C_{3}]$
1512.2.q.d	$1512$	$2$	1512.q	63.h	$3$	$22$	$11$	$12.073$		None					504.2.q.c	$2$	$0$	$0$	$0$	$-1$	$5$		$\mathrm{SU}(2)[C_{3}]$

Decomposition of $S_{2}^{\mathrm{old}}(1512, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(1512, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(63, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(126, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(189, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(252, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(378, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(504, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(756, [\chi])$$^{\oplus 2}$