Space of modular forms of level 576, weight 2, and Character 576.r

• Label: 576.2.r
• Level: $576$
• Weight: $2$
• Character orbit: 576.r
• Rep. character: $\chi_{576}(97,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $192$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(192\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(576, [\chi])\).

	Total	New	Old
Modular forms	216	48	168
Cusp forms	168	48	120
Eisenstein series	48	0	48

Trace form

\( 48 q + 24 q^{25} + 48 q^{33} - 24 q^{41} - 24 q^{49} + 24 q^{57} + 24 q^{81} - 96 q^{89}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(576, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
576.2.r.a	$576$	$2$	576.r	72.n	$6$	$4$	$2$	$4.599$	\(\Q(\zeta_{12})\)	None		✓			576.2.r.a	$4$	$1$	\(0\)	\(0\)	\(-12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
576.2.r.b	$576$	$2$	576.r	72.n	$6$	$4$	$2$	$4.599$	\(\Q(\zeta_{12})\)	None		✓			576.2.r.a	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
576.2.r.c	$576$	$2$	576.r	72.n	$6$	$8$	$4$	$4.599$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-2}) \)		✓			576.2.r.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{6}]$	\(q+(\beta_{6}-\beta_{4})q^{3}+(-\beta_{7}-\beta_{2}+\beta_1-1)q^{9}+\cdots\)
576.2.r.d	$576$	$2$	576.r	72.n	$6$	$8$	$4$	$4.599$	\(\Q(i, \sqrt{3}, \sqrt{5})\)	None		✓			576.2.r.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2\beta _{1}-\beta _{3})q^{3}-\beta _{4}q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)
576.2.r.e	$576$	$2$	576.r	72.n	$6$	$12$	$6$	$4.599$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			576.2.r.e	$4$	$0$	\(0\)	\(0\)	\(-18\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{4}+\beta _{5})q^{3}+(-2-\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
576.2.r.f	$576$	$2$	576.r	72.n	$6$	$12$	$6$	$4.599$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			576.2.r.e	$4$	$0$	\(0\)	\(0\)	\(18\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{4}+\beta _{5})q^{3}+(2+\beta _{6})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(576, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)