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

• Label: 760.2.bw
• Level: $760$
• Weight: $2$
• Character orbit: 760.bw
• Rep. character: $\chi_{760}(83,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $464$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.bw (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 760 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	496	496	0
Cusp forms	464	464	0
Eisenstein series	32	32	0

Trace form

464 * q - 2 * q^2 - 4 * q^3 - 8 * q^6 - 20 * q^8 - 2 * q^10 - 32 * q^11 - 20 * q^12 - 4 * q^17 - 32 * q^18 + 48 * q^20 - 26 * q^22 - 4 * q^25 + 16 * q^26 - 40 * q^27 - 4 * q^28 - 28 * q^30 - 12 * q^32 - 16 * q^33 - 52 * q^35 - 36 * q^36 - 62 * q^38 + 8 * q^40 - 8 * q^41 - 10 * q^42 - 4 * q^43 + 8 * q^46 + 24 * q^48 + 12 * q^50 + 8 * q^51 + 14 * q^52 - 16 * q^56 - 20 * q^57 + 124 * q^58 + 14 * q^60 - 8 * q^62 - 16 * q^65 - 60 * q^66 + 44 * q^67 + 4 * q^68 - 42 * q^70 - 28 * q^72 - 4 * q^73 - 240 * q^75 - 76 * q^76 - 12 * q^78 - 42 * q^80 + 160 * q^81 - 44 * q^82 + 64 * q^83 - 8 * q^86 - 120 * q^88 - 32 * q^90 - 8 * q^91 + 24 * q^92 - 208 * q^96 - 4 * q^97

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.bw.a	$760$	$2$	760.bw	760.aw	$12$	$8$	$2$	$6.069$	\(\Q(i, \sqrt{3}, \sqrt{10})\)	None		✓			760.2.bw.a	$8$	$0$	\(-4\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{2}-\beta _{4}+\beta _{6})q^{2}+(\beta _{2}-\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
760.2.bw.b	$760$	$2$	760.bw	760.aw	$12$	$456$	$114$	$6.069$		None		✓	✓		760.2.bw.b	$8$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$