Space of modular forms of level 240, weight 3, and Character 240.bd

• Label: 240.3.bd
• Level: $240$
• Weight: $3$
• Character orbit: 240.bd
• Rep. character: $\chi_{240}(203,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $184$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.bd (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 240 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(240, [\chi])\).

	Total	New	Old
Modular forms	200	200	0
Cusp forms	184	184	0
Eisenstein series	16	16	0

Trace form

184 * q + 4 * q^4 - 4 * q^6 - 8 * q^7 + 12 * q^10 + 16 * q^12 - 8 * q^13 - 36 * q^15 + 20 * q^16 + 20 * q^18 - 32 * q^19 - 4 * q^21 - 76 * q^22 - 36 * q^24 + 76 * q^28 + 36 * q^30 - 4 * q^33 + 28 * q^34 - 68 * q^36 - 8 * q^37 - 124 * q^40 + 56 * q^42 + 120 * q^43 + 48 * q^45 - 204 * q^46 - 112 * q^48 - 4 * q^51 - 32 * q^52 + 160 * q^54 - 8 * q^55 + 36 * q^57 + 180 * q^58 + 36 * q^60 + 24 * q^61 - 308 * q^64 - 212 * q^66 - 8 * q^67 - 36 * q^69 + 268 * q^70 - 344 * q^72 + 128 * q^75 - 372 * q^76 + 148 * q^78 - 8 * q^81 - 80 * q^82 + 96 * q^85 - 452 * q^87 + 44 * q^88 + 80 * q^90 - 8 * q^91 + 32 * q^93 + 188 * q^94 + 16 * q^96 - 8 * q^97 - 128 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(240, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
240.3.bd.a	$240$	$3$	240.bd	240.ad	$4$	$184$	$92$	$6.540$		None		✓	✓	✓	240.3.z.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{4}]$