Space of modular forms of level 240, weight 2, and Character 240.bc

• Label: 240.2.bc
• Level: $240$
• Weight: $2$
• Character orbit: 240.bc
• Rep. character: $\chi_{240}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $96$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bc (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(96\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(240, [\chi])\).

	Total	New	Old
Modular forms	104	48	56
Cusp forms	88	48	40
Eisenstein series	16	0	16

Trace form

\( 48 q + 4 q^{4} + 12 q^{8} - 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(240, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
240.2.bc.a	$240$	$2$	240.bc	80.j	$4$	$2$	$1$	$1.916$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-i)q^{2}-iq^{3}+2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
240.2.bc.b	$240$	$2$	240.bc	80.j	$4$	$2$	$1$	$1.916$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(-2\)	\(0\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-i)q^{2}+iq^{3}+2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
240.2.bc.c	$240$	$2$	240.bc	80.j	$4$	$2$	$1$	$1.916$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+i)q^{2}+iq^{3}+2iq^{4}+(-2-i)q^{5}+\cdots\)
240.2.bc.d	$240$	$2$	240.bc	80.j	$4$	$6$	$3$	$1.916$	6.0.399424.1	None		$2$	$0$	\(-2\)	\(0\)	\(12\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{2}-\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)
240.2.bc.e	$240$	$2$	240.bc	80.j	$4$	$16$	$8$	$1.916$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(2\)	\(0\)	\(-8\)	\(-4\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}-\beta _{5}q^{3}+(-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
240.2.bc.f	$240$	$2$	240.bc	80.j	$4$	$20$	$10$	$1.916$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(2\)	\(0\)	\(8\)	\(-4\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}-\beta _{15}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

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