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

• Label: 576.2.p
• Level: $576$
• Weight: $2$
• Character orbit: 576.p
• Rep. character: $\chi_{576}(95,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

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

\( 48 q - 24 q^{25} - 48 q^{33} + 72 q^{41} + 24 q^{49} + 24 q^{57} - 72 q^{81}+O(q^{100}) \)

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.p.a	$576$	$2$	576.p	72.l	$6$	$16$	$8$	$4.599$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			576.2.p.a	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{12}q^{3}+(\beta _{3}-\beta _{4}-\beta _{7})q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots\)
576.2.p.b	$576$	$2$	576.p	72.l	$6$	$16$	$8$	$4.599$	16.0.\(\cdots\).3	None		✓			576.2.p.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{3}+(\beta _{3}+\beta _{6})q^{5}+(-\beta _{14}-\beta _{15})q^{7}+\cdots\)
576.2.p.c	$576$	$2$	576.p	72.l	$6$	$16$	$8$	$4.599$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			576.2.p.a	$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{12}q^{3}+(-\beta _{3}+\beta _{4}+\beta _{7})q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)

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

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