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

• Label: 3024.2.ca
• Level: $3024$
• Weight: $2$
• Character orbit: 3024.ca
• Rep. character: $\chi_{3024}(2033,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $5$
• 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.ca (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1152\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

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

\( 92 q + 3 q^{5} + q^{7} + O(q^{10}) \)

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.ca.a	$3024$	$2$	3024.ca	63.i	$6$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(3-3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+(2+\cdots)q^{11}+\cdots\)
3024.2.ca.b	$3024$	$2$	3024.ca	63.i	$6$	$10$	$5$	$24.147$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{2}-\beta _{4}+\beta _{5}+\beta _{9})q^{5}+\cdots\)
3024.2.ca.c	$3024$	$2$	3024.ca	63.i	$6$	$16$	$8$	$24.147$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{6}+\beta _{10}-\beta _{11})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
3024.2.ca.d	$3024$	$2$	3024.ca	63.i	$6$	$16$	$8$	$24.147$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{9}q^{5}+(-\beta _{4}+\beta _{10})q^{7}+\beta _{15}q^{11}+\cdots\)
3024.2.ca.e	$3024$	$2$	3024.ca	63.i	$6$	$48$	$24$	$24.147$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 2}\)