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

• Label: 3024.2.k
• Level: $3024$
• Weight: $2$
• Character orbit: 3024.k
• Rep. character: $\chi_{3024}(1889,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $12$
• Sturm bound: $1152$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1152\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	612	64	548
Cusp forms	540	64	476
Eisenstein series	72	0	72

Trace form

\( 64 q + 2 q^{7} + 56 q^{25} - 32 q^{43} + 28 q^{67} - 60 q^{79} + 8 q^{85} - 42 q^{91}+O(q^{100}) \)

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.k.a	$3024$	$2$	3024.k	21.c	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None					756.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3 q^{5}+(-\beta-2)q^{7}+3\beta q^{11}+\cdots\)
3024.2.k.b	$3024$	$2$	3024.k	21.c	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					189.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta-1)q^{7}+(2\beta-1)q^{13}+(2\beta-1)q^{19}+\cdots\)
3024.2.k.c	$3024$	$2$	3024.k	21.c	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					756.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(2+\zeta_{6})q^{7}+(1-2\zeta_{6})q^{13}+(-5+\cdots)q^{19}+\cdots\)
3024.2.k.d	$3024$	$2$	3024.k	21.c	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None					756.2.f.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 q^{5}+(\beta-2)q^{7}+3\beta q^{11}-2\beta q^{13}+\cdots\)
3024.2.k.e	$3024$	$2$	3024.k	21.c	$2$	$4$	$4$	$24.147$	\(\Q(\zeta_{12})\)	None					378.2.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{5}+(\beta_1-2)q^{7}+\beta_{3} q^{11}+\cdots\)
3024.2.k.f	$3024$	$2$	3024.k	21.c	$2$	$4$	$4$	$24.147$	\(\Q(\zeta_{12})\)	None					378.2.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta_{2} q^{5}+(\beta_1-2)q^{7}+2\beta_{3} q^{11}+\cdots\)
3024.2.k.g	$3024$	$2$	3024.k	21.c	$2$	$4$	$4$	$24.147$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None					189.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(-1-\beta _{3})q^{7}-\beta _{1}q^{11}+\cdots\)
3024.2.k.h	$3024$	$2$	3024.k	21.c	$2$	$4$	$4$	$24.147$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None					756.2.f.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(1+\beta _{1})q^{7}+\beta _{3}q^{11}+\beta _{1}q^{13}+\cdots\)
3024.2.k.i	$3024$	$2$	3024.k	21.c	$2$	$4$	$4$	$24.147$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	None					189.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+(2-\beta _{2})q^{7}-\beta _{1}q^{11}-2\beta _{2}q^{13}+\cdots\)
3024.2.k.j	$3024$	$2$	3024.k	21.c	$2$	$4$	$4$	$24.147$	\(\Q(\zeta_{12})\)	None					378.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{5}+(-\beta_1+3)q^{7}+(-\beta_{3}+2\beta_{2})q^{11}+\cdots\)
3024.2.k.k	$3024$	$2$	3024.k	21.c	$2$	$16$	$16$	$24.147$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					1512.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{5}+\beta _{1}q^{7}+\beta _{10}q^{11}-\beta _{5}q^{13}+\cdots\)
3024.2.k.l	$3024$	$2$	3024.k	21.c	$2$	$16$	$16$	$24.147$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					1512.2.k.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{12}q^{7}-\beta _{10}q^{11}+(\beta _{4}+\cdots)q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 2}\)