Space of modular forms of level 760, weight 2, and Character 760.bi

• Label: 760.2.bi
• Level: $760$
• Weight: $2$
• Character orbit: 760.bi
• Rep. character: $\chi_{760}(331,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $160$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.bi (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(760, [\chi])\).

	Total	New	Old
Modular forms	248	160	88
Cusp forms	232	160	72
Eisenstein series	16	0	16

Trace form

160 * q - 2 * q^4 + 2 * q^6 + 80 * q^9 - 6 * q^10 + 2 * q^16 - 8 * q^19 + 12 * q^24 + 80 * q^25 - 4 * q^26 + 20 * q^28 - 16 * q^30 + 30 * q^32 - 6 * q^34 + 36 * q^36 - 10 * q^38 - 24 * q^41 + 2 * q^42 + 24 * q^44 - 18 * q^48 - 128 * q^49 + 24 * q^51 - 78 * q^52 - 38 * q^54 + 8 * q^57 + 4 * q^58 - 6 * q^60 - 32 * q^62 - 32 * q^64 - 12 * q^66 - 60 * q^68 - 36 * q^70 + 84 * q^72 - 16 * q^73 - 28 * q^74 - 32 * q^76 - 120 * q^78 - 72 * q^81 - 38 * q^82 - 96 * q^86 + 30 * q^90 - 80 * q^92 - 160 * q^96 - 6 * q^98 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(760, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
760.2.bi.a	$760$	$2$	760.bi	152.o	$6$	$160$	$80$	$6.069$		None		✓	✓	✓	760.2.bi.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(760, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)