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

• Label: 760.2.v
• Level: $760$
• Weight: $2$
• Character orbit: 760.v
• Rep. character: $\chi_{760}(113,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• 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.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(i)\)
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	256	60	196
Cusp forms	224	60	164
Eisenstein series	32	0	32

Trace form

\( 60 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
760.2.v.a	$760$	$2$	760.v	95.g	$4$	$12$	$6$	$6.069$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(-4\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{10}q^{3}+(-1-2\beta _{5})q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
760.2.v.b	$760$	$2$	760.v	95.g	$4$	$48$	$24$	$6.069$		None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(4\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 3}\)