Space of modular forms of level 2592, weight 2, and trivial character

• Label: 2592.2.a
• Level: $2592$
• Weight: $2$
• Character orbit: 2592.a
• Rep. character: $\chi_{2592}(1,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $24$
• Sturm bound: $864$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(864\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2592))\).

	Total	New	Old
Modular forms	480	48	432
Cusp forms	385	48	337
Eisenstein series	95	0	95

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

\(2\)	\(3\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(116\)	\(11\)	\(105\)		\(93\)	\(11\)	\(82\)		\(23\)	\(0\)	\(23\)
\(+\)	\(-\)	\(-\)		\(122\)	\(13\)	\(109\)		\(98\)	\(13\)	\(85\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(-\)		\(124\)	\(13\)	\(111\)		\(100\)	\(13\)	\(87\)		\(24\)	\(0\)	\(24\)
\(-\)	\(-\)	\(+\)		\(118\)	\(11\)	\(107\)		\(94\)	\(11\)	\(83\)		\(24\)	\(0\)	\(24\)
Plus space		\(+\)		\(234\)	\(22\)	\(212\)		\(187\)	\(22\)	\(165\)		\(47\)	\(0\)	\(47\)
Minus space		\(-\)		\(246\)	\(26\)	\(220\)		\(198\)	\(26\)	\(172\)		\(48\)	\(0\)	\(48\)

Trace form

\( 48 q + 48 q^{25} - 24 q^{37} + 48 q^{49} - 24 q^{61} + 24 q^{73} - 24 q^{85} + 24 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2592))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3
2592.2.a.a	$2592$	$2$	2592.a	1.a	$1$	$1$	$1$	$20.697$	\(\Q\)	None	✓				288.2.i.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-2q^{7}+5q^{11}-2q^{13}+3q^{17}+\cdots\)
2592.2.a.b	$2592$	$2$	2592.a	1.a	$1$	$1$	$1$	$20.697$	\(\Q\)	None	✓				288.2.i.a	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{7}-5q^{11}-2q^{13}+3q^{17}+\cdots\)
2592.2.a.c	$2592$	$2$	2592.a	1.a	$1$	$1$	$1$	$20.697$	\(\Q\)	None	✓	✓			2592.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+2q^{11}+q^{13}-3q^{17}+\cdots\)
2592.2.a.d	$2592$	$2$	2592.a	1.a	$1$	$1$	$1$	$20.697$	\(\Q\)	None	✓	✓			2592.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-2q^{11}+q^{13}-3q^{17}+\cdots\)
2592.2.a.e	$2592$	$2$	2592.a	1.a	$1$	$1$	$1$	$20.697$	\(\Q\)	None	✓	✓			2592.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-2q^{11}+q^{13}+3q^{17}+\cdots\)
2592.2.a.f	$2592$	$2$	2592.a	1.a	$1$	$1$	$1$	$20.697$	\(\Q\)	None	✓	✓			2592.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+2q^{11}+q^{13}+3q^{17}+\cdots\)
2592.2.a.g	$2592$	$2$	2592.a	1.a	$1$	$1$	$1$	$20.697$	\(\Q\)	None	✓				288.2.i.a	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-2q^{7}-5q^{11}-2q^{13}-3q^{17}+\cdots\)
2592.2.a.h	$2592$	$2$	2592.a	1.a	$1$	$1$	$1$	$20.697$	\(\Q\)	None	✓				288.2.i.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+2q^{7}+5q^{11}-2q^{13}-3q^{17}+\cdots\)
2592.2.a.i	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓	✓			2592.2.a.i	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+(-2+\beta )q^{5}+(3-2\beta )q^{13}+(-4+\cdots)q^{17}+\cdots\)
2592.2.a.j	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{6}) \)	None	✓				288.2.i.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
2592.2.a.k	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓	✓			2592.2.a.k	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$2$	$N(\mathrm{U}(1))$	\(q+(-1+\beta )q^{5}+(-3-\beta )q^{13}+(1-2\beta )q^{17}+\cdots\)
2592.2.a.l	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{3}) \)	None	✓				288.2.i.d	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}-\beta q^{11}-3q^{13}+4q^{17}+\cdots\)
2592.2.a.m	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{6}) \)	None	✓	✓			2592.2.a.m	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}-\beta q^{11}+3q^{13}-5q^{17}+\cdots\)
2592.2.a.n	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{6}) \)	None	✓				288.2.i.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta )q^{7}+(-1+\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
2592.2.a.o	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{6}) \)	None	✓				288.2.i.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
2592.2.a.p	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{3}) \)	None	✓				288.2.i.d	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}+\beta q^{11}-3q^{13}-4q^{17}+\cdots\)
2592.2.a.q	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓	✓			2592.2.a.k	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$2$	$N(\mathrm{U}(1))$	\(q+(1+\beta )q^{5}+(-3+\beta )q^{13}+(-1-2\beta )q^{17}+\cdots\)
2592.2.a.r	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{6}) \)	None	✓	✓			2592.2.a.m	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}+\beta q^{11}+3q^{13}+5q^{17}+\cdots\)
2592.2.a.s	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{6}) \)	None	✓				288.2.i.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+(1-\beta )q^{11}+(1+2\beta )q^{13}+\cdots\)
2592.2.a.t	$2592$	$2$	2592.a	1.a	$1$	$2$	$2$	$20.697$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-1}) \)	✓	✓			2592.2.a.i	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+(2+\beta )q^{5}+(3+2\beta )q^{13}+(4+\beta )q^{17}+\cdots\)
2592.2.a.u	$2592$	$2$	2592.a	1.a	$1$	$4$	$4$	$20.697$	\(\Q(\sqrt{18 +2 \sqrt{33}})\)	None	✓		✓		288.2.i.f	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{5}+\beta _{3}q^{7}-\beta _{2}q^{11}+\cdots\)
2592.2.a.v	$2592$	$2$	2592.a	1.a	$1$	$4$	$4$	$20.697$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	✓	✓		2592.2.a.v	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-1-\beta _{3})q^{11}+\cdots\)
2592.2.a.w	$2592$	$2$	2592.a	1.a	$1$	$4$	$4$	$20.697$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	✓			2592.2.a.v	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{3})q^{11}+\cdots\)
2592.2.a.x	$2592$	$2$	2592.a	1.a	$1$	$4$	$4$	$20.697$	\(\Q(\sqrt{18 +2 \sqrt{33}})\)	None	✓				288.2.i.f	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{5}+\beta _{3}q^{7}+\beta _{2}q^{11}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2592))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2592)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(648))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(864))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1296))\)\(^{\oplus 2}\)