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

• Label: 760.2.q
• Level: $760$
• Weight: $2$
• Character orbit: 760.q
• Rep. character: $\chi_{760}(121,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $7$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(240\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	256	40	216
Cusp forms	224	40	184
Eisenstein series	32	0	32

Trace form

\( 40 q + 6 q^{3} + 8 q^{7} - 26 q^{9} + O(q^{10}) \)

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.q.a	$760$	$2$	760.q	19.c	$3$	$2$	$1$	$6.069$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-2q^{7}+\cdots\)
760.2.q.b	$760$	$2$	760.q	19.c	$3$	$2$	$1$	$6.069$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-1\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+4q^{7}+\cdots\)
760.2.q.c	$760$	$2$	760.q	19.c	$3$	$2$	$1$	$6.069$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
760.2.q.d	$760$	$2$	760.q	19.c	$3$	$8$	$4$	$6.069$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(-1\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{3})q^{7}+(-4+\cdots)q^{9}+\cdots\)
760.2.q.e	$760$	$2$	760.q	19.c	$3$	$8$	$4$	$6.069$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(1-\beta _{5})q^{5}+(-1-\beta _{4}+2\beta _{7})q^{7}+\cdots\)
760.2.q.f	$760$	$2$	760.q	19.c	$3$	$8$	$4$	$6.069$	8.0.4601315889.1	None		$2$	$0$	\(0\)	\(1\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{7}q^{3}-\beta _{5}q^{5}+(-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
760.2.q.g	$760$	$2$	760.q	19.c	$3$	$10$	$5$	$6.069$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(1\)	\(5\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(1-\beta _{6})q^{5}+(1+\beta _{5})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)