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

• Label: 1512.2.k
• Level: $1512$
• Weight: $2$
• Character orbit: 1512.k
• Rep. character: $\chi_{1512}(377,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $25$

Defining parameters

Level:	$N$	$=$	$1512 = 2^{3} \cdot 3^{3} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1512.k (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$21$
Character field:			$\Q$
Newform subspaces:			$2$
Sturm bound:			$576$
Trace bound:			$25$
Distinguishing $T_p$:			$5$

Dimensions

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

	Total	New	Old
Modular forms	312	32	280
Cusp forms	264	32	232
Eisenstein series	48	0	48

Trace form

$32 q - 4 q^{7} + 24 q^{25} - 16 q^{37} + 28 q^{43} + 4 q^{49} + 16 q^{67} - 4 q^{79} + 32 q^{85} + 54 q^{91}+O(q^{100})$

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.k.a	$1512$	$2$	1512.k	21.c	$2$	$16$	$16$	$12.073$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			1512.2.k.a	$4$	$0$	$0$	$0$	$0$	$-2$	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{5}-\beta _{1}q^{7}-\beta _{10}q^{11}-\beta _{5}q^{13}+\cdots$
1512.2.k.b	$1512$	$2$	1512.k	21.c	$2$	$16$	$16$	$12.073$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			1512.2.k.b	$4$	$0$	$0$	$0$	$0$	$-2$	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{12}q^{7}+\beta _{10}q^{11}+(\beta _{4}+\cdots)q^{13}+\cdots$

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

$S_{2}^{\mathrm{old}}(1512, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(42, [\chi])$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(63, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(84, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(168, [\chi])$$^{\oplus 3}$$\oplus$$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}$