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

• Label: 760.2.p
• Level: $760$
• Weight: $2$
• Character orbit: 760.p
• Rep. character: $\chi_{760}(379,\cdot)$
• Character field: $\Q$
• Dimension: $116$
• Newform subspaces: $9$
• Sturm bound: $240$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 760 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(240\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(3\), \(7\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	124	124	0
Cusp forms	116	116	0
Eisenstein series	8	8	0

Trace form

116 * q - 8 * q^4 - 16 * q^6 + 100 * q^9 - 8 * q^11 - 8 * q^16 + 4 * q^19 - 12 * q^20 - 4 * q^25 + 16 * q^26 - 8 * q^30 - 40 * q^36 + 16 * q^44 + 84 * q^49 - 56 * q^54 - 56 * q^64 - 64 * q^66 - 40 * q^74 - 32 * q^80 + 52 * q^81 - 16 * q^96 - 136 * 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.p.a	$760$	$2$	760.p	760.p	$2$	$4$	$4$	$6.069$	\(\Q(\sqrt{-2}, \sqrt{5})\)	\(\Q(\sqrt{-10}) \)		✓			760.2.p.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}-2q^{4}-\beta _{3}q^{5}+2\beta _{3}q^{7}+\cdots\)
760.2.p.b	$760$	$2$	760.p	760.p	$2$	$4$	$4$	$6.069$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			760.2.p.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots\)
760.2.p.c	$760$	$2$	760.p	760.p	$2$	$4$	$4$	$6.069$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			760.2.p.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots\)
760.2.p.d	$760$	$2$	760.p	760.p	$2$	$8$	$8$	$6.069$	8.0.1499238400.2	None		✓			760.2.p.d	$4$	$0$	\(-8\)	\(-8\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{5})q^{2}-q^{3}+2\beta _{5}q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)
760.2.p.e	$760$	$2$	760.p	760.p	$2$	$8$	$8$	$6.069$	8.0.5473632256.3	None		✓			760.2.p.e	$4$	$0$	\(-4\)	\(8\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
760.2.p.f	$760$	$2$	760.p	760.p	$2$	$8$	$8$	$6.069$	8.0.5473632256.3	None		✓			760.2.p.e	$4$	$0$	\(4\)	\(-8\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}-q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
760.2.p.g	$760$	$2$	760.p	760.p	$2$	$8$	$8$	$6.069$	8.0.1499238400.2	None		✓			760.2.p.d	$4$	$0$	\(8\)	\(8\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{5})q^{2}+q^{3}+2\beta _{5}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
760.2.p.h	$760$	$2$	760.p	760.p	$2$	$16$	$16$	$6.069$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	\(\Q(\sqrt{-95}) \)		✓			760.2.p.h	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}+\cdots\)
760.2.p.i	$760$	$2$	760.p	760.p	$2$	$56$	$56$	$6.069$		None		✓	✓		760.2.p.i	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$