Space of modular forms of level 1440, weight 2, and Character 1440.q

• Label: 1440.2.q
• Level: $1440$
• Weight: $2$
• Character orbit: 1440.q
• Rep. character: $\chi_{1440}(481,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $96$
• Newform subspaces: $17$
• Sturm bound: $576$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(576\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1440, [\chi])\).

	Total	New	Old
Modular forms	608	96	512
Cusp forms	544	96	448
Eisenstein series	64	0	64

Trace form

\( 96 q - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1440.2.q.a	$1440$	$2$	1440.q	9.c	$3$	$2$	$1$	$11.498$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-3\)	\(-1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots\)
1440.2.q.b	$1440$	$2$	1440.q	9.c	$3$	$2$	$1$	$11.498$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-3\)	\(1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{7}+\cdots\)
1440.2.q.c	$1440$	$2$	1440.q	9.c	$3$	$2$	$1$	$11.498$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-3\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\cdots\)
1440.2.q.d	$1440$	$2$	1440.q	9.c	$3$	$2$	$1$	$11.498$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-3\)	\(1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots\)
1440.2.q.e	$1440$	$2$	1440.q	9.c	$3$	$2$	$1$	$11.498$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(-1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots\)
1440.2.q.f	$1440$	$2$	1440.q	9.c	$3$	$2$	$1$	$11.498$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots\)
1440.2.q.g	$1440$	$2$	1440.q	9.c	$3$	$2$	$1$	$11.498$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots\)
1440.2.q.h	$1440$	$2$	1440.q	9.c	$3$	$2$	$1$	$11.498$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(5-5\zeta_{6})q^{7}+\cdots\)
1440.2.q.i	$1440$	$2$	1440.q	9.c	$3$	$8$	$4$	$11.498$	8.0.3010058496.1	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{3}+\beta _{5}q^{5}+(\beta _{1}-\beta _{5}+\beta _{6})q^{7}+\cdots\)
1440.2.q.j	$1440$	$2$	1440.q	9.c	$3$	$8$	$4$	$11.498$	8.0.3317760000.8	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{7}q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
1440.2.q.k	$1440$	$2$	1440.q	9.c	$3$	$8$	$4$	$11.498$	8.0.121550625.1	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{5})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1440.2.q.l	$1440$	$2$	1440.q	9.c	$3$	$8$	$4$	$11.498$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\zeta_{24}^{5}+\zeta_{24}^{7})q^{3}+(-1+\zeta_{24}+\cdots)q^{5}+\cdots\)
1440.2.q.m	$1440$	$2$	1440.q	9.c	$3$	$8$	$4$	$11.498$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\zeta_{24}^{6}-\zeta_{24}^{7})q^{3}+\zeta_{24}q^{5}-\zeta_{24}^{7}q^{7}+\cdots\)
1440.2.q.n	$1440$	$2$	1440.q	9.c	$3$	$8$	$4$	$11.498$	8.0.3010058496.1	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{3}+\beta _{5}q^{5}+(-\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
1440.2.q.o	$1440$	$2$	1440.q	9.c	$3$	$10$	$5$	$11.498$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(-1\)	\(-5\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{3}-\beta _{2}q^{5}+(\beta _{4}+\beta _{5}+\beta _{6}+\beta _{7}+\cdots)q^{7}+\cdots\)
1440.2.q.p	$1440$	$2$	1440.q	9.c	$3$	$10$	$5$	$11.498$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(1\)	\(-5\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{3}-\beta _{2}q^{5}+(-\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
1440.2.q.q	$1440$	$2$	1440.q	9.c	$3$	$12$	$6$	$11.498$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{11}q^{3}+\beta _{3}q^{5}-\beta _{9}q^{7}-\beta _{10}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)