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

• Label: 2592.2.p
• Level: $2592$
• Weight: $2$
• Character orbit: 2592.p
• Rep. character: $\chi_{2592}(431,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $7$
• Sturm bound: $864$
• Trace bound: $41$

Defining parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(864\)
Trace bound:			\(41\)
Distinguishing \(T_p\):			\(5\), \(7\), \(41\)

Dimensions

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

	Total	New	Old
Modular forms	960	100	860
Cusp forms	768	92	676
Eisenstein series	192	8	184

Trace form

\( 92 q + 8 q^{19} - 34 q^{25} - 4 q^{43} + 38 q^{49} - 4 q^{67} - 8 q^{73} - 48 q^{91} + 4 q^{97}+O(q^{100}) \)

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.p.a	$2592$	$2$	2592.p	72.l	$6$	$4$	$2$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					72.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{3})q^{5}+(-2-2\beta _{2})q^{7}+\cdots\)
2592.2.p.b	$2592$	$2$	2592.p	72.l	$6$	$4$	$2$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)					24.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{1}q^{11}-2\beta _{3}q^{17}-2q^{19}+(5-5\beta _{2}+\cdots)q^{25}+\cdots\)
2592.2.p.c	$2592$	$2$	2592.p	72.l	$6$	$4$	$2$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					72.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{3})q^{5}+(2+2\beta _{2})q^{7}-2\beta _{1}q^{11}+\cdots\)
2592.2.p.d	$2592$	$2$	2592.p	72.l	$6$	$8$	$4$	$20.697$	8.0.170772624.1	None					216.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{6}q^{5}+(-\beta _{1}+\beta _{4})q^{7}-\beta _{3}q^{11}+\cdots\)
2592.2.p.e	$2592$	$2$	2592.p	72.l	$6$	$8$	$4$	$20.697$	8.0.170772624.1	None					216.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{6}q^{5}+(\beta _{1}-\beta _{4})q^{7}+\beta _{3}q^{11}+(2\beta _{2}+\cdots)q^{13}+\cdots\)
2592.2.p.f	$2592$	$2$	2592.p	72.l	$6$	$16$	$8$	$20.697$	16.0.\(\cdots\).1	None					216.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{12}q^{5}+(\beta _{9}+\beta _{15})q^{7}+(-\beta _{4}-\beta _{10}+\cdots)q^{11}+\cdots\)
2592.2.p.g	$2592$	$2$	2592.p	72.l	$6$	$48$	$24$	$20.697$		None			✓		648.2.f.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(2592, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)