Space of modular forms of level 1240, weight 2, and Character 1240.bm

• Label: 1240.2.bm
• Level: $1240$
• Weight: $2$
• Character orbit: 1240.bm
• Rep. character: $\chi_{1240}(129,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $384$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1240 = 2^{3} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1240.bm (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(384\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1240, [\chi])\).

	Total	New	Old
Modular forms	400	96	304
Cusp forms	368	96	272
Eisenstein series	32	0	32

Trace form

96 * q + 48 * q^9 + 12 * q^11 - 20 * q^15 - 8 * q^21 + 8 * q^25 - 24 * q^29 - 12 * q^31 + 4 * q^35 + 16 * q^39 + 60 * q^49 + 12 * q^51 + 2 * q^55 - 8 * q^59 + 24 * q^61 - 4 * q^69 + 8 * q^71 + 10 * q^75 + 84 * q^79 - 56 * q^81 - 40 * q^85 - 56 * q^89 - 96 * q^91 + 4 * q^95 - 56 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1240, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1240.2.bm.a	$1240$	$2$	1240.bm	155.j	$6$	$96$	$48$	$9.901$		None		✓	✓	✓	1240.2.bm.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1240, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(620, [\chi])\)\(^{\oplus 2}\)