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

• Label: 1596.2.r
• Level: $1596$
• Weight: $2$
• Character orbit: 1596.r
• Rep. character: $\chi_{1596}(457,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $640$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1596.r (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(640\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	664	48	616
Cusp forms	616	48	568
Eisenstein series	48	0	48

Trace form

48 * q - 2 * q^5 - 2 * q^7 - 24 * q^9 - 2 * q^11 - 8 * q^15 + 4 * q^17 - 4 * q^19 + 4 * q^23 - 22 * q^25 + 16 * q^29 - 4 * q^31 + 4 * q^33 - 6 * q^35 - 12 * q^37 - 8 * q^41 + 20 * q^43 - 2 * q^45 + 14 * q^47 - 2 * q^49 - 16 * q^51 - 40 * q^53 + 32 * q^55 + 8 * q^59 - 10 * q^61 + 10 * q^63 - 20 * q^65 + 16 * q^69 + 40 * q^71 - 38 * q^73 + 16 * q^75 + 26 * q^77 - 4 * q^79 - 24 * q^81 - 88 * q^83 + 100 * q^85 - 8 * q^87 + 8 * q^89 - 2 * q^95 - 104 * q^97 + 4 * q^99

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.r.a	$1596$	$2$	1596.r	7.c	$3$	$2$	$1$	$12.744$	\(\Q(\sqrt{-3}) \)	None		✓			1596.2.r.a	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
1596.2.r.b	$1596$	$2$	1596.r	7.c	$3$	$2$	$1$	$12.744$	\(\Q(\sqrt{-3}) \)	None		✓			1596.2.r.b	$2$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
1596.2.r.c	$1596$	$2$	1596.r	7.c	$3$	$2$	$1$	$12.744$	\(\Q(\sqrt{-3}) \)	None		✓			1596.2.r.c	$2$	$1$	\(0\)	\(-1\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1596.2.r.d	$1596$	$2$	1596.r	7.c	$3$	$2$	$1$	$12.744$	\(\Q(\sqrt{-3}) \)	None		✓			1596.2.r.d	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1596.2.r.e	$1596$	$2$	1596.r	7.c	$3$	$8$	$4$	$12.744$	8.0.6034027041.1	None		✓			1596.2.r.e	$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(-1+\beta _{2}-\beta _{6}+\beta _{7})q^{5}+\cdots\)
1596.2.r.f	$1596$	$2$	1596.r	7.c	$3$	$8$	$4$	$12.744$	8.0.447703281.1	None		✓			1596.2.r.f	$2$	$0$	\(0\)	\(-4\)	\(6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(2-2\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1596.2.r.g	$1596$	$2$	1596.r	7.c	$3$	$10$	$5$	$12.744$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1596.2.r.g	$2$	$0$	\(0\)	\(5\)	\(-5\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{6}q^{3}+(-1-\beta _{1}+\beta _{6})q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
1596.2.r.h	$1596$	$2$	1596.r	7.c	$3$	$14$	$7$	$12.744$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓	✓		1596.2.r.h	$2$	$0$	\(0\)	\(7\)	\(2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{8})q^{3}-\beta _{5}q^{5}-\beta _{12}q^{7}-\beta _{8}q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1596, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)