Space of modular forms of level 1584, weight 2, and Character 1584.o

• Label: 1584.2.o
• Level: $1584$
• Weight: $2$
• Character orbit: 1584.o
• Rep. character: $\chi_{1584}(703,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $7$
• Sturm bound: $576$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1584.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(576\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(83\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1584, [\chi])\).

	Total	New	Old
Modular forms	312	30	282
Cusp forms	264	30	234
Eisenstein series	48	0	48

Trace form

\( 30 q + 6 q^{25} + 30 q^{49} + 12 q^{53} + 48 q^{77} - 24 q^{89} + 48 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1584, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1584.2.o.a	$1584$	$2$	1584.o	44.c	$2$	$2$	$2$	$12.648$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)					176.2.e.a	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{5}-\beta q^{11}+\beta q^{23}+4q^{25}+3\beta q^{31}+\cdots\)
1584.2.o.b	$1584$	$2$	1584.o	44.c	$2$	$4$	$4$	$12.648$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			1584.2.o.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+\beta _{2}q^{7}+(-3+\beta _{1})q^{11}+\cdots\)
1584.2.o.c	$1584$	$2$	1584.o	44.c	$2$	$4$	$4$	$12.648$	\(\Q(\sqrt{6}, \sqrt{-11})\)	\(\Q(\sqrt{-33}) \)		✓			1584.2.o.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{7}-\beta _{3}q^{11}+\beta _{2}q^{17}+3\beta _{1}q^{19}+\cdots\)
1584.2.o.d	$1584$	$2$	1584.o	44.c	$2$	$4$	$4$	$12.648$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			1584.2.o.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+\beta _{2}q^{7}+(3-\beta _{1})q^{11}-3\beta _{1}q^{13}+\cdots\)
1584.2.o.e	$1584$	$2$	1584.o	44.c	$2$	$4$	$4$	$12.648$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)					176.2.e.b	$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(1+\beta _{3})q^{5}+(2\beta _{1}-\beta _{2})q^{11}+(\beta _{1}+\cdots)q^{23}+\cdots\)
1584.2.o.f	$1584$	$2$	1584.o	44.c	$2$	$4$	$4$	$12.648$	\(\Q(i, \sqrt{10})\)	None					528.2.o.a	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}+\beta _{3}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\cdots\)
1584.2.o.g	$1584$	$2$	1584.o	44.c	$2$	$8$	$8$	$12.648$	8.0.454201344.7	None			✓		528.2.o.b	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{5}+\beta _{6}q^{7}+(\beta _{3}-\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)