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

• Label: 3024.2.b
• Level: $3024$
• Weight: $2$
• Character orbit: 3024.b
• Rep. character: $\chi_{3024}(1567,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $22$
• Sturm bound: $1152$
• Trace bound: $47$

Defining parameters

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(1152\)
Trace bound:			\(47\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(19\), \(29\), \(47\)

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

\( 64 q + O(q^{10}) \)

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.b.a	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2-\zeta_{6})q^{7}+(-1+2\zeta_{6})q^{13}+\cdots\)
3024.2.b.b	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{5}+(-2+\zeta_{6})q^{7}+2\zeta_{6}q^{11}+\cdots\)
3024.2.b.c	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{5}+(-2+\zeta_{6})q^{7}-2\zeta_{6}q^{11}+\cdots\)
3024.2.b.d	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+2\zeta_{6}q^{11}+\cdots\)
3024.2.b.e	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}-2\zeta_{6}q^{11}+\cdots\)
3024.2.b.f	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1+\zeta_{6})q^{7}+(1-2\zeta_{6})q^{13}-7q^{19}+\cdots\)
3024.2.b.g	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+(3+\cdots)q^{11}+\cdots\)
3024.2.b.h	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+(3-6\zeta_{6})q^{11}+\cdots\)
3024.2.b.i	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+(-3+\cdots)q^{11}+\cdots\)
3024.2.b.j	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+(-3+\cdots)q^{11}+\cdots\)
3024.2.b.k	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{6}q^{7}+(-1+2\zeta_{6})q^{13}+7q^{19}+\cdots\)
3024.2.b.l	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}+2\zeta_{6}q^{11}+2\zeta_{6}q^{13}+\cdots\)
3024.2.b.m	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}-2\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots\)
3024.2.b.n	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+2\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots\)
3024.2.b.o	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}-2\zeta_{6}q^{11}+2\zeta_{6}q^{13}+\cdots\)
3024.2.b.p	$3024$	$2$	3024.b	28.d	$2$	$2$	$2$	$24.147$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(3-\zeta_{6})q^{7}+(1-2\zeta_{6})q^{13}-q^{19}+\cdots\)
3024.2.b.q	$3024$	$2$	3024.b	28.d	$2$	$4$	$4$	$24.147$	\(\Q(\sqrt{-6}, \sqrt{7})\)	\(\Q(\sqrt{-21}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}-\beta _{2}q^{7}-\beta _{1}q^{11}+(\beta _{1}-\beta _{3})q^{17}+\cdots\)
3024.2.b.r	$3024$	$2$	3024.b	28.d	$2$	$4$	$4$	$24.147$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{13}+\beta _{2}q^{17}+\cdots\)
3024.2.b.s	$3024$	$2$	3024.b	28.d	$2$	$4$	$4$	$24.147$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{5}+\beta _{1}q^{7}+\beta _{3}q^{13}+\beta _{2}q^{17}+\cdots\)
3024.2.b.t	$3024$	$2$	3024.b	28.d	$2$	$4$	$4$	$24.147$	\(\Q(\sqrt{-6}, \sqrt{7})\)	\(\Q(\sqrt{-21}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{1}q^{11}+(\beta _{1}-\beta _{3})q^{17}+\cdots\)
3024.2.b.u	$3024$	$2$	3024.b	28.d	$2$	$8$	$8$	$24.147$	8.0.\(\cdots\).13	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(-1-\beta _{5})q^{7}+\beta _{2}q^{11}+\cdots\)
3024.2.b.v	$3024$	$2$	3024.b	28.d	$2$	$8$	$8$	$24.147$	8.0.\(\cdots\).13	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(1-\beta _{5})q^{7}+\beta _{2}q^{11}+(-\beta _{3}+\cdots)q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \)