Space of modular forms of level 3024, weight 2, and Character 3024.cz

• Label: 3024.2.cz
• Level: $3024$
• Weight: $2$
• Character orbit: 3024.cz
• Rep. character: $\chi_{3024}(1279,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $9$
• Sturm bound: $1152$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cz (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 252 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1152\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3024, [\chi])\).

	Total	New	Old
Modular forms	1224	96	1128
Cusp forms	1080	96	984
Eisenstein series	144	0	144

Trace form

\( 96 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3024, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3024.2.cz.a	$3024$	$2$	3024.cz	252.aj	$6$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+3\zeta_{6})q^{7}+(4-2\zeta_{6})q^{11}+(-2+\cdots)q^{13}+\cdots\)
3024.2.cz.b	$3024$	$2$	3024.cz	252.aj	$6$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-3\zeta_{6})q^{7}+(-4+2\zeta_{6})q^{11}+(-2+\cdots)q^{13}+\cdots\)
3024.2.cz.c	$3024$	$2$	3024.cz	252.aj	$6$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+(6-3\zeta_{6})q^{11}+\cdots\)
3024.2.cz.d	$3024$	$2$	3024.cz	252.aj	$6$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+(-6+3\zeta_{6})q^{11}+\cdots\)
3024.2.cz.e	$3024$	$2$	3024.cz	252.aj	$6$	$4$	$2$	$24.147$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$1$	\(0\)	\(0\)	\(-6\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2-\beta _{1}+\beta _{3})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
3024.2.cz.f	$3024$	$2$	3024.cz	252.aj	$6$	$4$	$2$	$24.147$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2-\beta _{1}+\beta _{3})q^{5}+(1-\beta _{2})q^{7}+\cdots\)
3024.2.cz.g	$3024$	$2$	3024.cz	252.aj	$6$	$24$	$12$	$24.147$		None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-4\)		$\mathrm{SU}(2)[C_{6}]$
3024.2.cz.h	$3024$	$2$	3024.cz	252.aj	$6$	$24$	$12$	$24.147$		None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$\mathrm{SU}(2)[C_{6}]$
3024.2.cz.i	$3024$	$2$	3024.cz	252.aj	$6$	$32$	$16$	$24.147$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 2}\)