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

• Label: 1440.2.o
• Level: $1440$
• Weight: $2$
• Character orbit: 1440.o
• Rep. character: $\chi_{1440}(1439,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $43$

Defining parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(43\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	320	24	296
Cusp forms	256	24	232
Eisenstein series	64	0	64

Trace form

\( 24 q + O(q^{10}) \)

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.o.a	$1440$	$2$	1440.o	60.h	$2$	$12$	$12$	$11.498$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+\beta _{9}q^{7}+(-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)
1440.2.o.b	$1440$	$2$	1440.o	60.h	$2$	$12$	$12$	$11.498$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}-\beta _{9}q^{7}+(\beta _{2}-\beta _{3}-\beta _{4})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)