Space of modular forms of level 532, weight 2, and Character 532.j

• Label: 532.2.j
• Level: $532$
• Weight: $2$
• Character orbit: 532.j
• Rep. character: $\chi_{532}(197,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $20$
• Newform subspaces: $3$
• Sturm bound: $160$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(160\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(532, [\chi])\).

	Total	New	Old
Modular forms	172	20	152
Cusp forms	148	20	128
Eisenstein series	24	0	24

Trace form

20 * q - 2 * q^3 - 12 * q^9 + 4 * q^11 - 8 * q^13 + 6 * q^17 + 4 * q^21 + 8 * q^23 - 8 * q^25 - 8 * q^27 + 16 * q^29 - 16 * q^31 + 2 * q^35 - 4 * q^37 + 28 * q^39 - 22 * q^41 + 12 * q^43 - 84 * q^45 - 24 * q^47 + 20 * q^49 + 2 * q^51 + 26 * q^53 + 14 * q^55 + 32 * q^57 - 16 * q^59 + 16 * q^61 + 12 * q^63 + 16 * q^65 - 22 * q^67 + 56 * q^69 - 8 * q^75 - 8 * q^77 - 10 * q^79 - 22 * q^81 + 4 * q^83 + 8 * q^85 + 20 * q^87 - 4 * q^89 + 4 * q^91 - 4 * q^93 + 36 * q^95 + 4 * q^97 - 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(532, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
532.2.j.a	$532$	$2$	532.j	19.c	$3$	$2$	$1$	$4.248$	\(\Q(\sqrt{-3}) \)	None		✓			532.2.j.a	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+q^{7}+\cdots\)
532.2.j.b	$532$	$2$	532.j	19.c	$3$	$8$	$4$	$4.248$	8.0.\(\cdots\).2	None		✓			532.2.j.b	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{4})q^{3}+(-\beta _{1}-\beta _{6})q^{5}+\cdots\)
532.2.j.c	$532$	$2$	532.j	19.c	$3$	$10$	$5$	$4.248$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	✓		532.2.j.c	$2$	$0$	\(0\)	\(-3\)	\(-1\)	\(-10\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{6}+\beta _{8})q^{3}+(-\beta _{4}-\beta _{9})q^{5}-q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(532, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(532, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 2}\)