Space of modular forms of level 65, weight 2, and Character 65.b

• Label: 65.2.b
• Level: $65$
• Weight: $2$
• Character orbit: 65.b
• Rep. character: $\chi_{65}(14,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $14$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(14\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(65, [\chi])\).

	Total	New	Old
Modular forms	10	6	4
Cusp forms	6	6	0
Eisenstein series	4	0	4

Trace form

6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 + 16 * q^15 + 10 * q^16 - 20 * q^20 - 4 * q^21 + 16 * q^24 + 2 * q^25 - 6 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 + 20 * q^34 + 8 * q^35 - 22 * q^36 + 8 * q^39 - 34 * q^40 - 8 * q^41 + 40 * q^44 - 4 * q^45 + 32 * q^46 + 18 * q^49 + 16 * q^50 + 24 * q^51 - 68 * q^54 - 16 * q^55 + 40 * q^56 + 16 * q^59 - 12 * q^60 + 12 * q^61 - 66 * q^64 - 2 * q^65 - 16 * q^66 - 24 * q^69 - 20 * q^70 - 24 * q^71 + 4 * q^74 + 16 * q^75 - 20 * q^76 + 32 * q^79 + 48 * q^80 + 46 * q^81 + 12 * q^84 - 12 * q^85 - 32 * q^86 - 20 * q^89 + 70 * q^90 - 4 * q^91 - 32 * q^94 + 16 * q^95 - 36 * q^96 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(65, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
65.2.b.a	$65$	$2$	65.b	5.b	$2$	$6$	$6$	$0.519$	6.0.350464.1	None		✓	✓	✓	65.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)