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

• Label: 576.2.bb
• Level: $576$
• Weight: $2$
• Character orbit: 576.bb
• Rep. character: $\chi_{576}(49,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $88$
• Newform subspaces: $5$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	416	104	312
Cusp forms	352	88	264
Eisenstein series	64	16	48

Trace form

88 * q + 4 * q^3 - 2 * q^5 + 2 * q^11 - 2 * q^13 + 8 * q^15 - 16 * q^17 + 8 * q^19 - 10 * q^21 - 8 * q^27 - 2 * q^29 + 4 * q^31 - 8 * q^33 + 28 * q^35 - 8 * q^37 + 2 * q^43 - 14 * q^45 + 44 * q^47 + 16 * q^49 + 36 * q^51 - 8 * q^53 - 10 * q^59 - 2 * q^61 + 36 * q^63 - 4 * q^65 + 2 * q^67 - 10 * q^69 - 56 * q^75 - 30 * q^77 + 4 * q^79 - 8 * q^81 + 22 * q^83 - 12 * q^85 + 36 * q^91 - 22 * q^93 - 60 * q^95 - 4 * q^97 - 10 * q^99

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.bb.a	$576$	$2$	576.bb	144.x	$12$	$4$	$1$	$4.599$	\(\Q(\zeta_{12})\)	None					144.2.x.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1-\zeta_{12}+\cdots)q^{5}+\cdots\)
576.2.bb.b	$576$	$2$	576.bb	144.x	$12$	$4$	$1$	$4.599$	\(\Q(\zeta_{12})\)	None					144.2.x.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-2\zeta_{12}^{2})q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots\)
576.2.bb.c	$576$	$2$	576.bb	144.x	$12$	$4$	$1$	$4.599$	\(\Q(\zeta_{12})\)	None					144.2.x.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots\)
576.2.bb.d	$576$	$2$	576.bb	144.x	$12$	$4$	$1$	$4.599$	\(\Q(\zeta_{12})\)	None					144.2.x.b	$2$	$0$	\(0\)	\(6\)	\(-8\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(2-\zeta_{12}^{2})q^{3}+(-2-2\zeta_{12}+2\zeta_{12}^{3})q^{5}+\cdots\)
576.2.bb.e	$576$	$2$	576.bb	144.x	$12$	$72$	$18$	$4.599$		None			✓		144.2.x.e	$4$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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