Space of modular forms of level 1596, weight 2, and Character 1596.s

• Label: 1596.2.s
• Level: $1596$
• Weight: $2$
• Character orbit: 1596.s
• Rep. character: $\chi_{1596}(505,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $6$
• Sturm bound: $640$
• Trace bound: $5$

Defining parameters

Level:	$N$	$=$	$1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1596.s (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$19$
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$6$
Sturm bound:			$640$
Trace bound:			$5$
Distinguishing $T_p$:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(1596, [\chi])$.

	Total	New	Old
Modular forms	664	40	624
Cusp forms	616	40	576
Eisenstein series	48	0	48

Trace form

40 * q - 20 * q^9 + 8 * q^13 - 4 * q^15 - 4 * q^17 + 8 * q^19 - 4 * q^21 - 24 * q^23 - 24 * q^25 + 4 * q^29 + 32 * q^31 - 4 * q^33 - 4 * q^35 + 16 * q^37 + 8 * q^41 + 4 * q^43 + 20 * q^47 + 40 * q^49 - 8 * q^51 - 20 * q^53 - 36 * q^55 + 16 * q^57 + 20 * q^59 - 16 * q^61 + 48 * q^65 + 8 * q^67 + 8 * q^69 + 8 * q^71 - 4 * q^73 + 16 * q^75 + 16 * q^77 + 12 * q^79 - 20 * q^81 + 8 * q^83 + 16 * q^87 - 8 * q^89 - 8 * q^91 - 16 * q^93 - 80 * q^95 - 12 * q^97

Decomposition of $S_{2}^{\mathrm{new}}(1596, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1596.2.s.a	$1596$	$2$	1596.s	19.c	$3$	$2$	$1$	$12.744$	$\Q(\sqrt{-3})$	None		✓			1596.2.s.a	$2$	$1$	$0$	$-1$	$-1$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+q^{7}+\cdots$
1596.2.s.b	$1596$	$2$	1596.s	19.c	$3$	$2$	$1$	$12.744$	$\Q(\sqrt{-3})$	None		✓			1596.2.s.b	$2$	$0$	$0$	$-1$	$3$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+q^{7}+\cdots$
1596.2.s.c	$1596$	$2$	1596.s	19.c	$3$	$8$	$4$	$12.744$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			1596.2.s.c	$2$	$0$	$0$	$-4$	$-6$	$8$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{3})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots$
1596.2.s.d	$1596$	$2$	1596.s	19.c	$3$	$8$	$4$	$12.744$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			1596.2.s.d	$2$	$0$	$0$	$-4$	$2$	$-8$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{7})q^{5}+\cdots$
1596.2.s.e	$1596$	$2$	1596.s	19.c	$3$	$8$	$4$	$12.744$	8.0.2127515625.3	None		✓			1596.2.s.e	$2$	$0$	$0$	$4$	$2$	$8$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{3}+\beta _{1}q^{5}+q^{7}+(-1-\beta _{5}+\cdots)q^{9}+\cdots$
1596.2.s.f	$1596$	$2$	1596.s	19.c	$3$	$12$	$6$	$12.744$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		1596.2.s.f	$2$	$0$	$0$	$6$	$0$	$-12$	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{3}-\beta _{3}q^{5}-q^{7}-\beta _{2}q^{9}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(1596, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(1596, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(38, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(57, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(76, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(114, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(133, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(228, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(266, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(399, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(532, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(798, [\chi])$$^{\oplus 2}$