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

• Label: 576.2.d
• Level: $576$
• Weight: $2$
• Character orbit: 576.d
• Rep. character: $\chi_{576}(289,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(17\)
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	10	110
Cusp forms	72	10	62
Eisenstein series	48	0	48

Trace form

\( 10 q - 12 q^{17} + 2 q^{25} + 36 q^{41} + 26 q^{49} - 28 q^{73} - 60 q^{89} - 44 q^{97}+O(q^{100}) \)

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.d.a	$576$	$2$	576.d	8.b	$2$	$2$	$2$	$4.599$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-2}) \)					64.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+3\beta q^{11}+6 q^{17}+\beta q^{19}+5 q^{25}+\cdots\)
576.2.d.b	$576$	$2$	576.d	8.b	$2$	$4$	$4$	$4.599$	\(\Q(\zeta_{12})\)	None					192.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{5}-\beta_1 q^{7}-6 q^{17}-\beta_{3} q^{19}+\cdots\)
576.2.d.c	$576$	$2$	576.d	8.b	$2$	$4$	$4$	$4.599$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		✓			576.2.d.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta_1 q^{7}-\beta_{2} q^{13}-\beta_{3} q^{19}+5 q^{25}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(576, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)