Space of modular forms of level 576, weight 3, and Character 576.g

• Label: 576.3.g
• Level: $576$
• Weight: $3$
• Character orbit: 576.g
• Rep. character: $\chi_{576}(127,\cdot)$
• Character field: $\Q$
• Dimension: $19$
• Newform subspaces: $10$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(576, [\chi])\).

	Total	New	Old
Modular forms	216	21	195
Cusp forms	168	19	149
Eisenstein series	48	2	46

Trace form

\( 19 q - 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
576.3.g.a	$576$	$3$	576.g	4.b	$2$	$1$	$1$	$15.695$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-8q^{5}+10q^{13}-2^{4}q^{17}+39q^{25}+\cdots\)
576.3.g.b	$576$	$3$	576.g	4.b	$2$	$1$	$1$	$15.695$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-6q^{5}-10q^{13}+30q^{17}+11q^{25}+\cdots\)
576.3.g.c	$576$	$3$	576.g	4.b	$2$	$1$	$1$	$15.695$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+8q^{5}+10q^{13}+2^{4}q^{17}+39q^{25}+\cdots\)
576.3.g.d	$576$	$3$	576.g	4.b	$2$	$2$	$2$	$15.695$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-4q^{5}+iq^{7}-4iq^{11}+2q^{13}+24q^{17}+\cdots\)
576.3.g.e	$576$	$3$	576.g	4.b	$2$	$2$	$2$	$15.695$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{5}-\zeta_{6}q^{7}+\zeta_{6}q^{11}-2q^{13}+\cdots\)
576.3.g.f	$576$	$3$	576.g	4.b	$2$	$2$	$2$	$15.695$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{6}q^{7}-22q^{13}+2\zeta_{6}q^{19}-5^{2}q^{25}+\cdots\)
576.3.g.g	$576$	$3$	576.g	4.b	$2$	$2$	$2$	$15.695$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}+2iq^{7}+iq^{11}+14q^{13}+\cdots\)
576.3.g.h	$576$	$3$	576.g	4.b	$2$	$2$	$2$	$15.695$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+4q^{5}+iq^{7}+4iq^{11}+2q^{13}-24q^{17}+\cdots\)
576.3.g.i	$576$	$3$	576.g	4.b	$2$	$2$	$2$	$15.695$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+6q^{5}-\zeta_{6}q^{7}+3\zeta_{6}q^{11}+14q^{13}+\cdots\)
576.3.g.j	$576$	$3$	576.g	4.b	$2$	$4$	$4$	$15.695$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\zeta_{12}^{2})q^{5}+(\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)