Space of modular forms of level 1080, weight 2, and Character 1080.q

• Label: 1080.2.q
• Level: $1080$
• Weight: $2$
• Character orbit: 1080.q
• Rep. character: $\chi_{1080}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $432$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(432\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1080, [\chi])\).

	Total	New	Old
Modular forms	480	24	456
Cusp forms	384	24	360
Eisenstein series	96	0	96

Trace form

24 * q + 2 * q^5 - 2 * q^11 - 28 * q^17 - 12 * q^19 - 12 * q^25 + 6 * q^29 + 12 * q^31 + 24 * q^35 + 4 * q^41 + 18 * q^43 - 12 * q^47 - 6 * q^49 - 8 * q^53 - 2 * q^59 + 6 * q^61 + 8 * q^65 + 6 * q^67 + 8 * q^71 + 36 * q^73 + 40 * q^77 - 32 * q^83 + 36 * q^89 - 24 * q^91 - 18 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1080, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1080.2.q.a	$1080$	$2$	1080.q	9.c	$3$	$2$	$1$	$8.624$	\(\Q(\sqrt{-3}) \)	None					360.2.q.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{11}-3q^{17}+\cdots\)
1080.2.q.b	$1080$	$2$	1080.q	9.c	$3$	$4$	$2$	$8.624$	\(\Q(\zeta_{12})\)	None					360.2.q.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_1-1)q^{5}+(\beta_{2}-2\beta_1)q^{7}+(-2\beta_{2}+2\beta_1)q^{11}+\cdots\)
1080.2.q.c	$1080$	$2$	1080.q	9.c	$3$	$4$	$2$	$8.624$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					360.2.q.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+2q^{17}+\cdots\)
1080.2.q.d	$1080$	$2$	1080.q	9.c	$3$	$6$	$3$	$8.624$	6.0.954288.1	None					360.2.q.d	$2$	$0$	\(0\)	\(0\)	\(3\)	\(5\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{5}+(1-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5})q^{7}+\cdots\)
1080.2.q.e	$1080$	$2$	1080.q	9.c	$3$	$8$	$4$	$8.624$	8.0.856615824.2	None			✓		360.2.q.e	$2$	$0$	\(0\)	\(0\)	\(4\)	\(1\)	$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{5}+\beta _{2}q^{7}+(-\beta _{2}+\beta _{6}-\beta _{7})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1080, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)