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

• Label: 240.2.f
• Level: $240$
• Weight: $2$
• Character orbit: 240.f
• Rep. character: $\chi_{240}(49,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	60	6	54
Cusp forms	36	6	30
Eisenstein series	24	0	24

Trace form

6 * q + 2 * q^5 - 6 * q^9 + 16 * q^19 + 6 * q^25 - 4 * q^29 + 8 * q^31 - 24 * q^35 - 8 * q^39 - 12 * q^41 - 2 * q^45 - 6 * q^49 - 16 * q^51 + 8 * q^55 + 16 * q^59 + 12 * q^61 - 8 * q^65 - 8 * q^69 - 16 * q^71 + 8 * q^75 - 40 * q^79 + 6 * q^81 + 8 * q^85 + 28 * q^89 - 16 * q^91 + 32 * q^95

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.f.a	$240$	$2$	240.f	5.b	$2$	$2$	$2$	$1.916$	\(\Q(\sqrt{-1}) \)	None					30.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(i-2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
240.2.f.b	$240$	$2$	240.f	5.b	$2$	$2$	$2$	$1.916$	\(\Q(\sqrt{-1}) \)	None					60.2.d.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-2 i+1)q^{5}-4 i q^{7}+\cdots\)
240.2.f.c	$240$	$2$	240.f	5.b	$2$	$2$	$2$	$1.916$	\(\Q(\sqrt{-1}) \)	None					120.2.f.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(i+2)q^{5}+2 i q^{7}-q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(240, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)