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

• Label: 576.2.s
• Level: $576$
• Weight: $2$
• Character orbit: 576.s
• Rep. character: $\chi_{576}(191,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $44$
• Newform subspaces: $7$
• Sturm bound: $192$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(192\)
Trace bound:			\(7\)
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	216	52	164
Cusp forms	168	44	124
Eisenstein series	48	8	40

Trace form

44 * q + 6 * q^5 - 4 * q^9 + 2 * q^13 + 10 * q^21 + 12 * q^25 + 6 * q^29 - 14 * q^33 + 8 * q^37 - 30 * q^41 + 38 * q^45 + 8 * q^49 + 2 * q^61 - 6 * q^65 - 26 * q^69 - 8 * q^73 + 6 * q^77 + 4 * q^81 - 8 * q^85 + 34 * q^93 - 2 * q^97

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.s.a	$576$	$2$	576.s	36.h	$6$	$2$	$1$	$4.599$	\(\Q(\sqrt{-3}) \)	None					144.2.s.a	$2$	$0$	\(0\)	\(-3\)	\(6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+\cdots\)
576.2.s.b	$576$	$2$	576.s	36.h	$6$	$2$	$1$	$4.599$	\(\Q(\sqrt{-3}) \)	None					144.2.s.b	$2$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
576.2.s.c	$576$	$2$	576.s	36.h	$6$	$2$	$1$	$4.599$	\(\Q(\sqrt{-3}) \)	None					144.2.s.b	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(1+\zeta_{6})q^{7}+\cdots\)
576.2.s.d	$576$	$2$	576.s	36.h	$6$	$2$	$1$	$4.599$	\(\Q(\sqrt{-3}) \)	None					144.2.s.a	$2$	$0$	\(0\)	\(3\)	\(6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(-2-2\zeta_{6})q^{7}+\cdots\)
576.2.s.e	$576$	$2$	576.s	36.h	$6$	$4$	$2$	$4.599$	\(\Q(\zeta_{12})\)	None					144.2.s.e	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta_{3} q^{3}+(\beta_1-2)q^{5}+(-\beta_{3}-\beta_{2})q^{7}+\cdots\)
576.2.s.f	$576$	$2$	576.s	36.h	$6$	$8$	$4$	$4.599$	8.0.170772624.1	None					36.2.h.a	$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{6}q^{3}+(1+\beta _{2})q^{5}+(\beta _{1}-\beta _{6})q^{7}+\cdots\)
576.2.s.g	$576$	$2$	576.s	36.h	$6$	$24$	$12$	$4.599$		None			✓		288.2.s.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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