Space of modular forms of level 1584, weight 2, and trivial character

• Label: 1584.2.a
• Level: $1584$
• Weight: $2$
• Character orbit: 1584.a
• Rep. character: $\chi_{1584}(1,\cdot)$
• Character field: $\Q$
• Dimension: $25$
• Newform subspaces: $22$
• Sturm bound: $576$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1584.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(576\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1584))\).

	Total	New	Old
Modular forms	312	25	287
Cusp forms	265	25	240
Eisenstein series	47	0	47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(11\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(5\)
\(+\)	\(-\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(4\)
Plus space			\(+\)	\(11\)
Minus space			\(-\)	\(14\)

Trace form

\( 25 q - 2 q^{5} - 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1584))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	11
1584.2.a.a	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots\)
1584.2.a.b	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots\)
1584.2.a.c	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}-q^{11}+6q^{13}+4q^{17}+\cdots\)
1584.2.a.d	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{11}+2q^{13}-6q^{17}+4q^{23}+\cdots\)
1584.2.a.e	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}+q^{11}-2q^{13}-4q^{17}+\cdots\)
1584.2.a.f	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}-q^{11}-6q^{13}-2q^{17}+\cdots\)
1584.2.a.g	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+q^{11}+4q^{13}+2q^{17}+\cdots\)
1584.2.a.h	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-q^{11}-4q^{13}+6q^{17}+4q^{19}+\cdots\)
1584.2.a.i	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots\)
1584.2.a.j	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+q^{11}+2q^{17}-8q^{19}-2q^{23}+\cdots\)
1584.2.a.k	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\)
1584.2.a.l	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-q^{11}-6q^{13}-6q^{17}+2q^{19}+\cdots\)
1584.2.a.m	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+q^{11}-6q^{13}+6q^{17}+2q^{19}+\cdots\)
1584.2.a.n	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}-q^{11}+6q^{13}-6q^{17}+\cdots\)
1584.2.a.o	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots\)
1584.2.a.p	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-2q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots\)
1584.2.a.q	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots\)
1584.2.a.r	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+2q^{7}-q^{11}-2q^{13}-2q^{17}+\cdots\)
1584.2.a.s	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+2q^{7}+q^{11}+4q^{13}+2q^{17}+\cdots\)
1584.2.a.t	$1584$	$2$	1584.a	1.a	$1$	$2$	$2$	$12.648$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(2-2\beta )q^{7}-q^{11}+\cdots\)
1584.2.a.u	$1584$	$2$	1584.a	1.a	$1$	$2$	$2$	$12.648$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2-\beta )q^{7}-q^{11}+(2-\beta )q^{13}+\cdots\)
1584.2.a.v	$1584$	$2$	1584.a	1.a	$1$	$2$	$2$	$12.648$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2+\beta )q^{7}+q^{11}+(2+\beta )q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1584))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1584)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 2}\)