Space of modular forms of level 576, weight 8, and Character 576.c

• Label: 576.8.c
• Level: $576$
• Weight: $8$
• Character orbit: 576.c
• Rep. character: $\chi_{576}(575,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $7$
• Sturm bound: $768$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	576.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(768\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(576, [\chi])\).

	Total	New	Old
Modular forms	696	56	640
Cusp forms	648	56	592
Eisenstein series	48	0	48

Trace form

\( 56 q + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(576, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
576.8.c.a	$576$	$8$	576.c	12.b	$2$	$2$	$2$	$179.934$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+83\beta q^{5}-13108q^{13}-5713\beta q^{17}+\cdots\)
576.8.c.b	$576$	$8$	576.c	12.b	$2$	$2$	$2$	$179.934$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+307\beta q^{5}+13108q^{13}+22955\beta q^{17}+\cdots\)
576.8.c.c	$576$	$8$	576.c	12.b	$2$	$4$	$4$	$179.934$	\(\Q(\sqrt{-2}, \sqrt{-555})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+65\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}+10868q^{13}+\cdots\)
576.8.c.d	$576$	$8$	576.c	12.b	$2$	$8$	$8$	$179.934$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{3}-\beta _{4})q^{5}+(\beta _{1}-\beta _{5})q^{7}+(-\beta _{6}+\cdots)q^{11}+\cdots\)
576.8.c.e	$576$	$8$	576.c	12.b	$2$	$12$	$12$	$179.934$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{68}\cdot 3^{20}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{6}-3\beta _{7})q^{5}-\beta _{9}q^{7}+\beta _{1}q^{11}+\cdots\)
576.8.c.f	$576$	$8$	576.c	12.b	$2$	$12$	$12$	$179.934$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{53}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-37\beta _{4}+\beta _{8})q^{5}+(-5\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
576.8.c.g	$576$	$8$	576.c	12.b	$2$	$16$	$16$	$179.934$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{98}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-7\beta _{8}+\beta _{12})q^{5}+\beta _{4}q^{7}+(-3\beta _{9}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(576, [\chi]) \cong \)