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

• Label: 1596.2.u
• Level: $1596$
• Weight: $2$
• Character orbit: 1596.u
• Rep. character: $\chi_{1596}(145,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $52$
• Newform subspaces: $3$
• Sturm bound: $640$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1596.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(640\)
Trace bound:			\(1\)
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	52	612
Cusp forms	616	52	564
Eisenstein series	48	0	48

Trace form

52 * q + q^7 - 26 * q^9 - 6 * q^11 - 3 * q^13 - 12 * q^17 - 9 * q^19 + 3 * q^21 - 64 * q^25 + 3 * q^31 + 16 * q^35 - 3 * q^37 - 3 * q^39 - 12 * q^41 + 13 * q^43 - 6 * q^45 - 6 * q^47 - 25 * q^49 + 12 * q^55 - 13 * q^57 + 24 * q^59 + 24 * q^61 - 2 * q^63 + 36 * q^65 - 24 * q^69 + 24 * q^71 - 45 * q^73 - 22 * q^77 - 26 * q^81 + 2 * q^85 - 30 * q^91 - 14 * q^93 + 16 * q^95 - 6 * q^97 - 6 * 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.u.a	$1596$	$2$	1596.u	133.i	$6$	$2$	$1$	$12.744$	\(\Q(\sqrt{-3}) \)	None		✓			1596.2.u.a	$2$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{6}q^{3}+(-1+2\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
1596.2.u.b	$1596$	$2$	1596.u	133.i	$6$	$24$	$12$	$12.744$		None		✓			1596.2.u.b	$2$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1596.2.u.c	$1596$	$2$	1596.u	133.i	$6$	$26$	$13$	$12.744$		None		✓	✓		1596.2.u.c	$2$	$0$	\(0\)	\(13\)	\(0\)	\(5\)		$\mathrm{SU}(2)[C_{6}]$

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

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