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

• Label: 240.2.o
• Level: $240$
• Weight: $2$
• Character orbit: 240.o
• Rep. character: $\chi_{240}(239,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	60	12	48
Cusp forms	36	12	24
Eisenstein series	24	0	24

Trace form

\( 12 q + 12 q^{21} - 12 q^{25} - 12 q^{45} - 12 q^{49} - 48 q^{61} - 12 q^{69} - 60 q^{81} + 48 q^{85}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
240.2.o.a	$240$	$2$	240.o	60.h	$2$	$4$	$4$	$1.916$	\(\Q(\sqrt{2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)		✓			240.2.o.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(-2+\cdots)q^{9}+\cdots\)
240.2.o.b	$240$	$2$	240.o	60.h	$2$	$8$	$8$	$1.916$	\(\Q(\zeta_{24})\)	None		✓	✓		240.2.o.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{3}-\beta_1 q^{5}+(\beta_{4}-\beta_1+1)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(240, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)