Space of modular forms of level 240, weight 3, and Character 240.l

• Label: 240.3.l
• Level: $240$
• Weight: $3$
• Character orbit: 240.l
• Rep. character: $\chi_{240}(161,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(240, [\chi])\).

	Total	New	Old
Modular forms	108	16	92
Cusp forms	84	16	68
Eisenstein series	24	0	24

Trace form

\( 16 q - 16 q^{7} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(240, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
240.3.l.a	$240$	$3$	240.l	3.b	$2$	$2$	$2$	$6.540$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\beta )q^{3}-\beta q^{5}-2q^{7}+(-1+\cdots)q^{9}+\cdots\)
240.3.l.b	$240$	$3$	240.l	3.b	$2$	$2$	$2$	$6.540$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta )q^{3}-\beta q^{5}+6q^{7}+(-1+4\beta )q^{9}+\cdots\)
240.3.l.c	$240$	$3$	240.l	3.b	$2$	$4$	$4$	$6.540$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2+\cdots)q^{7}+\cdots\)
240.3.l.d	$240$	$3$	240.l	3.b	$2$	$8$	$8$	$6.540$	8.0.\(\cdots\).5	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-16\)	$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{6}q^{5}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)