Space of modular forms of level 240, weight 4, and Character 240.bc

• Label: 240.4.bc
• Level: $240$
• Weight: $4$
• Character orbit: 240.bc
• Rep. character: $\chi_{240}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $144$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	240.bc (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(240, [\chi])\).

	Total	New	Old
Modular forms	296	144	152
Cusp forms	280	144	136
Eisenstein series	16	0	16

Trace form

\( 144 q - 12 q^{4} - 84 q^{8} - 1296 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(240, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
240.4.bc.a	$240$	$4$	240.bc	80.j	$4$	$72$	$36$	$14.160$		None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
240.4.bc.b	$240$	$4$	240.bc	80.j	$4$	$72$	$36$	$14.160$		None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)