Space of modular forms of level 576, weight 4, and Character 576.d

• Label: 576.4.d
• Level: $576$
• Weight: $4$
• Character orbit: 576.d
• Rep. character: $\chi_{576}(289,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $8$
• Sturm bound: $384$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	576.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(384\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(576, [\chi])\).

	Total	New	Old
Modular forms	312	30	282
Cusp forms	264	30	234
Eisenstein series	48	0	48

Trace form

\( 30 q + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(576, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
576.4.d.a	$576$	$4$	576.d	8.b	$2$	$2$	$2$	$33.985$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+9iq^{11}-90q^{17}-53iq^{19}+5^{3}q^{25}+\cdots\)
576.4.d.b	$576$	$4$	576.d	8.b	$2$	$4$	$4$	$33.985$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}+6\zeta_{12}^{3}q^{11}+\cdots\)
576.4.d.c	$576$	$4$	576.d	8.b	$2$	$4$	$4$	$33.985$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{5}-7\zeta_{12}q^{7}+12\zeta_{12}^{3}q^{11}+\cdots\)
576.4.d.d	$576$	$4$	576.d	8.b	$2$	$4$	$4$	$33.985$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{12}^{2}q^{7}+\zeta_{12}^{3}q^{13}-7\zeta_{12}q^{19}+\cdots\)
576.4.d.e	$576$	$4$	576.d	8.b	$2$	$4$	$4$	$33.985$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+21\zeta_{12}q^{11}+\cdots\)
576.4.d.f	$576$	$4$	576.d	8.b	$2$	$4$	$4$	$33.985$	\(\Q(i, \sqrt{11})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+\beta _{2}q^{7}+12\beta _{1}q^{11}-4\beta _{3}q^{13}+\cdots\)
576.4.d.g	$576$	$4$	576.d	8.b	$2$	$4$	$4$	$33.985$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}+2^{4}\zeta_{12}^{2}q^{13}+\cdots\)
576.4.d.h	$576$	$4$	576.d	8.b	$2$	$4$	$4$	$33.985$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}+6\zeta_{12}^{3}q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

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