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

• Label: 576.2.c
• Level: $576$
• Weight: $2$
• Character orbit: 576.c
• Rep. character: $\chi_{576}(575,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	120	8	112
Cusp forms	72	8	64
Eisenstein series	48	0	48

Trace form

\( 8 q - 16 q^{13} - 8 q^{25} + 16 q^{37} - 8 q^{49} + 48 q^{61} - 32 q^{85} - 32 q^{97}+O(q^{100}) \)

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.c.a	$576$	$2$	576.c	12.b	$2$	$2$	$2$	$4.599$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)					144.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-4q^{13}+\beta q^{17}-13q^{25}+\cdots\)
576.2.c.b	$576$	$2$	576.c	12.b	$2$	$2$	$2$	$4.599$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)					36.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}+4q^{13}+5\beta q^{17}+3q^{25}+\cdots\)
576.2.c.c	$576$	$2$	576.c	12.b	$2$	$4$	$4$	$4.599$	\(\Q(\zeta_{8})\)	None			✓		288.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{5}+\beta_1 q^{7}+\beta_{3} q^{11}-4 q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(576, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)