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

• Label: 3024.2.r
• Level: $3024$
• Weight: $2$
• Character orbit: 3024.r
• Rep. character: $\chi_{3024}(1009,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $14$
• Sturm bound: $1152$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.r (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(1152\)
Trace bound:			\(11\)
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	72	1152
Cusp forms	1080	72	1008
Eisenstein series	144	0	144

Trace form

\( 72 q + 12 q^{11} - 8 q^{17} - 12 q^{23} - 36 q^{25} - 24 q^{35} - 4 q^{41} - 12 q^{47} - 36 q^{49} + 12 q^{59} + 8 q^{65} + 80 q^{71} + 24 q^{73} + 16 q^{89} - 32 q^{95} - 12 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3024.2.r.a	$3024$	$2$	3024.r	9.c	$3$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None					126.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
3024.2.r.b	$3024$	$2$	3024.r	9.c	$3$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None					504.2.r.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
3024.2.r.c	$3024$	$2$	3024.r	9.c	$3$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None					126.2.f.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
3024.2.r.d	$3024$	$2$	3024.r	9.c	$3$	$2$	$1$	$24.147$	\(\Q(\sqrt{-3}) \)	None					504.2.r.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
3024.2.r.e	$3024$	$2$	3024.r	9.c	$3$	$4$	$2$	$24.147$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					126.2.f.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+(-2+\cdots)q^{11}+\cdots\)
3024.2.r.f	$3024$	$2$	3024.r	9.c	$3$	$4$	$2$	$24.147$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					126.2.f.d	$2$	$0$	\(0\)	\(0\)	\(3\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{3})q^{5}+(1-\beta _{1})q^{7}+(-1+2\beta _{1}+\cdots)q^{11}+\cdots\)
3024.2.r.g	$3024$	$2$	3024.r	9.c	$3$	$6$	$3$	$24.147$	6.0.309123.1	None					63.2.f.b	$2$	$0$	\(0\)	\(0\)	\(-5\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}-\beta _{3}-2\beta _{4})q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots\)
3024.2.r.h	$3024$	$2$	3024.r	9.c	$3$	$6$	$3$	$24.147$	\(\Q(\zeta_{18})\)	None					504.2.r.c	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_{2}-\beta_1)q^{5}+(-\beta_1+1)q^{7}+\cdots\)
3024.2.r.i	$3024$	$2$	3024.r	9.c	$3$	$6$	$3$	$24.147$	6.0.309123.1	None					252.2.j.b	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}+\beta _{3})q^{5}+\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots\)
3024.2.r.j	$3024$	$2$	3024.r	9.c	$3$	$6$	$3$	$24.147$	6.0.309123.1	None					252.2.j.a	$2$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{5})q^{5}+(-1+\beta _{4})q^{7}+(-1+\cdots)q^{11}+\cdots\)
3024.2.r.k	$3024$	$2$	3024.r	9.c	$3$	$6$	$3$	$24.147$	\(\Q(\zeta_{18})\)	None					63.2.f.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_{5}-\beta_{4}-\beta_{3}+\beta_1)q^{5}+(-\beta_1+1)q^{7}+\cdots\)
3024.2.r.l	$3024$	$2$	3024.r	9.c	$3$	$8$	$4$	$24.147$	8.0.508277025.1	None					504.2.r.d	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}+\beta _{4}-\beta _{5}+\beta _{7})q^{5}-\beta _{5}q^{7}+\cdots\)
3024.2.r.m	$3024$	$2$	3024.r	9.c	$3$	$8$	$4$	$24.147$	8.0.2091141441.1	None					504.2.r.e	$2$	$0$	\(0\)	\(0\)	\(3\)	\(-4\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2}+\beta _{3})q^{5}+\beta _{3}q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
3024.2.r.n	$3024$	$2$	3024.r	9.c	$3$	$10$	$5$	$24.147$	10.0.\(\cdots\).1	None			✓		504.2.r.f	$2$	$0$	\(0\)	\(0\)	\(3\)	\(-5\)	$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{7})q^{5}+\beta _{1}q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 2}\)