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

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