Space of modular forms of level 715, weight 2, and Character 715.bf

• Label: 715.2.bf
• Level: $715$
• Weight: $2$
• Character orbit: 715.bf
• Rep. character: $\chi_{715}(64,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $320$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 715 = 5 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	715.bf (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 715 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(715, [\chi])\).

	Total	New	Old
Modular forms	352	352	0
Cusp forms	320	320	0
Eisenstein series	32	32	0

Trace form

320 * q - 88 * q^4 + 48 * q^9 - 16 * q^10 - 16 * q^14 - 48 * q^16 + 6 * q^25 - 20 * q^26 - 44 * q^29 - 24 * q^30 + 32 * q^35 + 212 * q^36 - 2 * q^39 - 30 * q^40 - 96 * q^49 + 6 * q^55 + 128 * q^56 - 72 * q^64 + 40 * q^65 - 92 * q^66 + 32 * q^69 - 60 * q^74 - 94 * q^75 - 60 * q^79 - 56 * q^81 - 196 * q^90 + 112 * q^94 + 22 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(715, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
715.2.bf.a	$715$	$2$	715.bf	715.af	$10$	$320$	$80$	$5.709$		None		✓	✓	✓	715.2.bf.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$