Space of modular forms of level 1584, weight 3, and Character 1584.j

• Label: 1584.3.j
• Level: $1584$
• Weight: $3$
• Character orbit: 1584.j
• Rep. character: $\chi_{1584}(1297,\cdot)$
• Character field: $\Q$
• Dimension: $59$
• Newform subspaces: $13$
• Sturm bound: $864$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1584.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(864\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1584, [\chi])\).

	Total	New	Old
Modular forms	600	61	539
Cusp forms	552	59	493
Eisenstein series	48	2	46

Trace form

\( 59 q + 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1584, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1584.3.j.a	$1584$	$3$	1584.j	11.b	$2$	$1$	$1$	$43.161$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+q^{5}-11q^{11}+35q^{23}-24q^{25}+\cdots\)
1584.3.j.b	$1584$	$3$	1584.j	11.b	$2$	$2$	$2$	$43.161$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q-4q^{5}+\beta q^{7}+11q^{11}-4\beta q^{13}+\cdots\)
1584.3.j.c	$1584$	$3$	1584.j	11.b	$2$	$2$	$2$	$43.161$	\(\Q(\sqrt{33}) \)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1-\beta )q^{5}-11q^{11}+(-19-3\beta )q^{23}+\cdots\)
1584.3.j.d	$1584$	$3$	1584.j	11.b	$2$	$2$	$2$	$43.161$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{5}+\beta q^{7}+(7+\beta )q^{11}+\beta q^{13}+\cdots\)
1584.3.j.e	$1584$	$3$	1584.j	11.b	$2$	$2$	$2$	$43.161$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+4q^{5}-\beta q^{7}-11q^{11}+4\beta q^{13}+\cdots\)
1584.3.j.f	$1584$	$3$	1584.j	11.b	$2$	$4$	$4$	$43.161$	4.0.39744.5	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-3\beta _{1})q^{5}-\beta _{2}q^{7}+(5+\beta _{1}+\cdots)q^{11}+\cdots\)
1584.3.j.g	$1584$	$3$	1584.j	11.b	$2$	$4$	$4$	$43.161$	4.0.131904.1	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+(5-3\beta _{1}+\cdots)q^{11}+\cdots\)
1584.3.j.h	$1584$	$3$	1584.j	11.b	$2$	$4$	$4$	$43.161$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{2}q^{7}+(-\beta _{1}-\beta _{3})q^{11}+\cdots\)
1584.3.j.i	$1584$	$3$	1584.j	11.b	$2$	$4$	$4$	$43.161$	\(\Q(\sqrt{-3}, \sqrt{46})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{3}q^{7}+(-\beta _{1}+5\beta _{2})q^{11}+\cdots\)
1584.3.j.j	$1584$	$3$	1584.j	11.b	$2$	$4$	$4$	$43.161$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-4\beta _{2})q^{5}+(\beta _{1}+2\beta _{3})q^{7}+(-4+\cdots)q^{11}+\cdots\)
1584.3.j.k	$1584$	$3$	1584.j	11.b	$2$	$6$	$6$	$43.161$	6.0.1750426112.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}-\beta _{4}q^{7}+(2+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots\)
1584.3.j.l	$1584$	$3$	1584.j	11.b	$2$	$12$	$12$	$43.161$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}-\beta _{5}q^{7}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
1584.3.j.m	$1584$	$3$	1584.j	11.b	$2$	$12$	$12$	$43.161$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{2}q^{7}+\beta _{7}q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1584, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)