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

• Label: 2592.2.r
• Level: $2592$
• Weight: $2$
• Character orbit: 2592.r
• Rep. character: $\chi_{2592}(433,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $17$
• Sturm bound: $864$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(864\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(13\), \(17\)

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

\( 92 q - 4 q^{7} + 42 q^{25} - 4 q^{31} - 30 q^{49} - 32 q^{55} - 8 q^{73} - 4 q^{79} + 4 q^{97}+O(q^{100}) \)

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.r.a	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\zeta_{12})\)	None					648.2.d.e	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{12}-\zeta_{12}^{2})q^{5}+(\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
2592.2.r.b	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\zeta_{12})\)	None					648.2.d.e	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{12}-\zeta_{12}^{2})q^{5}+(\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
2592.2.r.c	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					648.2.d.g	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
2592.2.r.d	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					648.2.d.g	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
2592.2.r.e	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None					648.2.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{5}-2\beta _{2}q^{7}-\beta _{1}q^{13}-7q^{17}+\cdots\)
2592.2.r.f	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\zeta_{12})\)	None					24.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_1 q^{5}-2\beta_{2} q^{7}-2\beta_1 q^{13}+\cdots\)
2592.2.r.g	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\zeta_{12})\)	None					24.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_1 q^{5}-2\beta_{2} q^{7}+2\beta_1 q^{13}+\cdots\)
2592.2.r.h	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None					648.2.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{5}-2\beta _{2}q^{7}+\beta _{1}q^{13}+7q^{17}+\cdots\)
2592.2.r.i	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)					72.2.d.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{1}q^{5}+2\beta _{2}q^{7}+(-2\beta _{1}+2\beta _{3})q^{11}+\cdots\)
2592.2.r.j	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\zeta_{12})\)	None					648.2.d.e	$2$	$0$	\(0\)	\(0\)	\(6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{12}+\zeta_{12}^{2})q^{5}+(\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
2592.2.r.k	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\zeta_{12})\)	None					648.2.d.e	$2$	$0$	\(0\)	\(0\)	\(6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{12}+\zeta_{12}^{2})q^{5}+(\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
2592.2.r.l	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					648.2.d.g	$2$	$0$	\(0\)	\(0\)	\(6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2+\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(2+\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
2592.2.r.m	$2592$	$2$	2592.r	72.n	$6$	$4$	$2$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					648.2.d.g	$2$	$0$	\(0\)	\(0\)	\(6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2+\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(2+\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
2592.2.r.n	$2592$	$2$	2592.r	72.n	$6$	$8$	$4$	$20.697$	\(\Q(i, \sqrt{3}, \sqrt{5})\)	None					648.2.d.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{7})q^{5}-4\beta _{2}q^{7}+2\beta _{1}q^{11}+\cdots\)
2592.2.r.o	$2592$	$2$	2592.r	72.n	$6$	$8$	$4$	$20.697$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-6}) \)					216.2.d.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}\cdot 3^{4}$	$\mathrm{U}(1)[D_{6}]$	\(q+(\beta_{4}-\beta_{3}+\beta_1)q^{5}+(\beta_{7}-\beta_{6}+\beta_{2}-1)q^{7}+\cdots\)
2592.2.r.p	$2592$	$2$	2592.r	72.n	$6$	$8$	$4$	$20.697$	\(\Q(i, \sqrt{3}, \sqrt{7})\)	None					216.2.d.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{5}+(1-\beta _{3})q^{7}-3\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\)
2592.2.r.q	$2592$	$2$	2592.r	72.n	$6$	$16$	$8$	$20.697$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		216.2.d.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{4}+\beta _{7})q^{5}+\beta _{5}q^{7}-\beta _{14}q^{11}+\cdots\)

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

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