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

• Label: 3024.2.t
• Level: $3024$
• Weight: $2$
• Character orbit: 3024.t
• Rep. character: $\chi_{3024}(289,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $92$
• Newform subspaces: $12$
• 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.t (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 12 \)
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	100	1124
Cusp forms	1080	92	988
Eisenstein series	144	8	136

Trace form

\( 92 q + 2 q^{5} + q^{7} + O(q^{10}) \)

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.t.a	$3024$	$2$	3024.t	63.g	$3$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3q^{5}+(-3+\zeta_{6})q^{7}-3q^{11}+(1+\cdots)q^{13}+\cdots\)
3024.2.t.b	$3024$	$2$	3024.t	63.g	$3$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2q^{5}+(-3+2\zeta_{6})q^{7}+4q^{11}+(-3+\cdots)q^{13}+\cdots\)
3024.2.t.c	$3024$	$2$	3024.t	63.g	$3$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{5}+(3-\zeta_{6})q^{7}-3q^{11}+(-1+\zeta_{6})q^{13}+\cdots\)
3024.2.t.d	$3024$	$2$	3024.t	63.g	$3$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{5}+(1-3\zeta_{6})q^{7}+5q^{11}+(5-5\zeta_{6})q^{13}+\cdots\)
3024.2.t.e	$3024$	$2$	3024.t	63.g	$3$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{5}+(-1+3\zeta_{6})q^{7}+3q^{11}+(-3+\cdots)q^{13}+\cdots\)
3024.2.t.f	$3024$	$2$	3024.t	63.g	$3$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3q^{5}+(-1+3\zeta_{6})q^{7}-3q^{11}+(-5+\cdots)q^{13}+\cdots\)
3024.2.t.g	$3024$	$2$	3024.t	63.g	$3$	$6$	$3$	$24.147$	6.0.309123.1	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-\beta _{1})q^{5}+(\beta _{1}+\beta _{2}+\beta _{4})q^{7}+\cdots\)
3024.2.t.h	$3024$	$2$	3024.t	63.g	$3$	$6$	$3$	$24.147$	6.0.309123.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{5}+(1+\beta _{1}-\beta _{2}-\beta _{5})q^{7}-\beta _{3}q^{11}+\cdots\)
3024.2.t.i	$3024$	$2$	3024.t	63.g	$3$	$10$	$5$	$24.147$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(1\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2}+\beta _{9})q^{5}+(\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots\)
3024.2.t.j	$3024$	$2$	3024.t	63.g	$3$	$14$	$7$	$24.147$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(3\)	$3^{7}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{3}-\beta _{7})q^{5}+\beta _{5}q^{7}+(-\beta _{9}+\beta _{13})q^{11}+\cdots\)
3024.2.t.k	$3024$	$2$	3024.t	63.g	$3$	$22$	$11$	$24.147$		None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$\mathrm{SU}(2)[C_{3}]$
3024.2.t.l	$3024$	$2$	3024.t	63.g	$3$	$22$	$11$	$24.147$		None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(-7\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)