Space of modular forms of level 2592, weight 2, and Character 2592.s

• Label: 2592.2.s
• Level: $2592$
• Weight: $2$
• Character orbit: 2592.s
• Rep. character: $\chi_{2592}(863,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $10$
• Sturm bound: $864$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(864\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2592, [\chi])\).

	Total	New	Old
Modular forms	960	96	864
Cusp forms	768	96	672
Eisenstein series	192	0	192

Trace form

\( 96 q + 48 q^{25} + 48 q^{49} - 48 q^{73} - 24 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2592, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2592.2.s.a	$2592$	$2$	2592.s	36.h	$6$	$8$	$4$	$20.697$	\(\Q(\zeta_{24})\)	None					864.2.c.a	$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{5}+\beta_{2}-2)q^{5}+(-\beta_{7}-\beta_{4}+\beta_1)q^{7}+\cdots\)
2592.2.s.b	$2592$	$2$	2592.s	36.h	$6$	$8$	$4$	$20.697$	\(\Q(\zeta_{24})\)	None		✓			2592.2.c.a	$4$	$1$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{24}-\zeta_{24}^{5}+\zeta_{24}^{7})q^{5}+(-2-\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)
2592.2.s.c	$2592$	$2$	2592.s	36.h	$6$	$8$	$4$	$20.697$	\(\Q(\zeta_{24})\)	None					864.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_{6} q^{5}+(-\beta_{4}+\beta_{2}+\beta_1-2)q^{7}+\cdots\)
2592.2.s.d	$2592$	$2$	2592.s	36.h	$6$	$8$	$4$	$20.697$	\(\Q(\zeta_{24})\)	None					288.2.c.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta_{4} q^{5}+\beta_1 q^{7}+(\beta_{7}-\beta_{6})q^{11}+\cdots\)
2592.2.s.e	$2592$	$2$	2592.s	36.h	$6$	$8$	$4$	$20.697$	\(\Q(\zeta_{24})\)	None					96.2.c.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_{5} q^{5}-\beta_1 q^{7}+(-\beta_{7}+\beta_{4})q^{11}+\cdots\)
2592.2.s.f	$2592$	$2$	2592.s	36.h	$6$	$8$	$4$	$20.697$	\(\Q(\zeta_{24})\)	None		✓			2592.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{24}-\zeta_{24}^{5}+\zeta_{24}^{7})q^{5}+(2+\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)
2592.2.s.g	$2592$	$2$	2592.s	36.h	$6$	$8$	$4$	$20.697$	\(\Q(\zeta_{24})\)	None					864.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_{6} q^{5}+(\beta_{4}-\beta_{2}-\beta_1+2)q^{7}+\cdots\)
2592.2.s.h	$2592$	$2$	2592.s	36.h	$6$	$8$	$4$	$20.697$	\(\Q(\zeta_{24})\)	None					864.2.c.a	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta_{5}-\beta_{2}+2)q^{5}+(-\beta_{7}-\beta_{4}+\beta_1)q^{7}+\cdots\)
2592.2.s.i	$2592$	$2$	2592.s	36.h	$6$	$16$	$8$	$20.697$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			2592.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{5}-\beta _{9}+\beta _{12}+\beta _{14}+\beta _{15})q^{5}+\cdots\)
2592.2.s.j	$2592$	$2$	2592.s	36.h	$6$	$16$	$8$	$20.697$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			2592.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{5}-\beta _{9}+\beta _{12}+\beta _{14}+\beta _{15})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2592, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2592, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)