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

• Label: 2592.2.i
• Level: $2592$
• Weight: $2$
• Character orbit: 2592.i
• Rep. character: $\chi_{2592}(865,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $96$
• Newform subspaces: $34$
• Sturm bound: $864$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 34 \)
Sturm bound:			\(864\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

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.i.a	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-1}) \)					288.2.a.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q-4\zeta_{6}q^{5}+6\zeta_{6}q^{13}+8q^{17}+(-11+\cdots)q^{25}+\cdots\)
2592.2.i.b	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					96.2.a.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
2592.2.i.c	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
2592.2.i.d	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.e	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-1}) \)					32.2.a.a	$4$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q-2\zeta_{6}q^{5}-6\zeta_{6}q^{13}-2q^{17}+(1-\zeta_{6})q^{25}+\cdots\)
2592.2.i.f	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.g	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
2592.2.i.h	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					96.2.a.a	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
2592.2.i.i	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.e	$2$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2592.2.i.j	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None		✓			2592.2.a.c	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.k	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None		✓			2592.2.a.c	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.l	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.e	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
2592.2.i.m	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.e	$2$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
2592.2.i.n	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None		✓			2592.2.a.c	$2$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.o	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None		✓			2592.2.a.c	$2$	$0$	\(0\)	\(0\)	\(1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.p	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.e	$2$	$0$	\(0\)	\(0\)	\(1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2592.2.i.q	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					96.2.a.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
2592.2.i.r	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
2592.2.i.s	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2592.2.i.t	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-1}) \)					32.2.a.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+2\zeta_{6}q^{5}-6\zeta_{6}q^{13}+2q^{17}+(1-\zeta_{6})q^{25}+\cdots\)
2592.2.i.u	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2592.2.i.v	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					864.2.a.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
2592.2.i.w	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	None					96.2.a.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
2592.2.i.x	$2592$	$2$	2592.i	9.c	$3$	$2$	$1$	$20.697$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-1}) \)					288.2.a.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+4\zeta_{6}q^{5}+6\zeta_{6}q^{13}-8q^{17}+(-11+\cdots)q^{25}+\cdots\)
2592.2.i.y	$2592$	$2$	2592.i	9.c	$3$	$4$	$2$	$20.697$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		✓			2592.2.a.i	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$3$	$\mathrm{U}(1)[D_{3}]$	\(q+(\beta_{2}-2\beta_1)q^{5}+(2\beta_{2}-3\beta_1)q^{13}+\cdots\)
2592.2.i.z	$2592$	$2$	2592.i	9.c	$3$	$4$	$2$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			2592.2.a.m	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1})q^{5}+\beta _{2}q^{7}+\beta _{2}q^{11}+\cdots\)
2592.2.i.ba	$2592$	$2$	2592.i	9.c	$3$	$4$	$2$	$20.697$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		✓			2592.2.a.k	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{3}]$	\(q+(\beta_{2}-\beta_1)q^{5}+(\beta_{2}+3\beta_1)q^{13}+\cdots\)
2592.2.i.bb	$2592$	$2$	2592.i	9.c	$3$	$4$	$2$	$20.697$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None					864.2.a.m	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2592.2.i.bc	$2592$	$2$	2592.i	9.c	$3$	$4$	$2$	$20.697$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None					864.2.a.m	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
2592.2.i.bd	$2592$	$2$	2592.i	9.c	$3$	$4$	$2$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			2592.2.a.m	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+\beta _{2}q^{11}+(-3+\cdots)q^{13}+\cdots\)
2592.2.i.be	$2592$	$2$	2592.i	9.c	$3$	$4$	$2$	$20.697$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		✓			2592.2.a.k	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{3}]$	\(q+(-\beta_{2}+\beta_1)q^{5}+(\beta_{2}+3\beta_1)q^{13}+\cdots\)
2592.2.i.bf	$2592$	$2$	2592.i	9.c	$3$	$4$	$2$	$20.697$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		✓			2592.2.a.i	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$3$	$\mathrm{U}(1)[D_{3}]$	\(q+(\beta_{3}-\beta_{2}-2\beta_1+2)q^{5}+(-2\beta_{3}+2\beta_{2}+\cdots-3)q^{13}+\cdots\)
2592.2.i.bg	$2592$	$2$	2592.i	9.c	$3$	$8$	$4$	$20.697$	8.0.49787136.1	None		✓			2592.2.a.v	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{5}+(\beta _{4}-\beta _{7})q^{7}+(-\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots\)
2592.2.i.bh	$2592$	$2$	2592.i	9.c	$3$	$8$	$4$	$20.697$	8.0.49787136.1	None		✓			2592.2.a.v	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{5}+(-\beta _{4}+\beta _{7})q^{7}+(\beta _{2}+\beta _{5}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2592, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)