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

• Label: 65.2.f
• Level: $65$
• Weight: $2$
• Character orbit: 65.f
• Rep. character: $\chi_{65}(18,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $14$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(14\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	18	18	0
Cusp forms	10	10	0
Eisenstein series	8	8	0

Trace form

10 * q - 4 * q^3 - 6 * q^4 - 6 * q^5 - 4 * q^6 - 4 * q^7 + 8 * q^10 + 4 * q^11 + 10 * q^13 - 4 * q^15 - 10 * q^16 + 14 * q^17 + 18 * q^18 - 4 * q^19 - 6 * q^20 - 16 * q^21 + 8 * q^22 - 20 * q^23 + 4 * q^24 - 6 * q^25 + 12 * q^26 + 20 * q^27 - 12 * q^28 - 16 * q^30 + 12 * q^31 - 2 * q^34 - 16 * q^35 - 44 * q^37 + 8 * q^38 - 4 * q^39 + 28 * q^40 + 2 * q^41 + 20 * q^42 - 4 * q^43 - 12 * q^44 + 24 * q^45 + 8 * q^46 + 28 * q^47 - 16 * q^48 + 18 * q^49 + 36 * q^50 - 42 * q^52 - 14 * q^53 + 12 * q^54 + 16 * q^55 + 24 * q^58 - 8 * q^59 - 16 * q^60 - 8 * q^61 - 40 * q^62 + 34 * q^64 + 2 * q^65 - 40 * q^66 + 2 * q^68 - 8 * q^69 - 72 * q^70 - 8 * q^71 - 22 * q^72 + 44 * q^75 + 16 * q^76 - 20 * q^77 + 4 * q^78 - 22 * q^80 - 10 * q^81 + 34 * q^82 + 60 * q^83 - 20 * q^84 + 38 * q^85 - 48 * q^86 + 16 * q^87 - 16 * q^88 + 18 * q^89 - 10 * q^90 + 28 * q^91 + 44 * q^92 - 20 * q^93 - 28 * q^95 + 40 * q^96

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.f.a	$65$	$2$	65.f	65.f	$4$	$2$	$1$	$0.519$	\(\Q(\sqrt{-1}) \)	None		✓			65.2.f.a	$2$	$0$	\(0\)	\(2\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+i q^{2}+(-i+1)q^{3}+q^{4}+(-i-2)q^{5}+\cdots\)
65.2.f.b	$65$	$2$	65.f	65.f	$4$	$8$	$4$	$0.519$	8.0.619810816.2	None		✓	✓		65.2.f.b	$2$	$0$	\(0\)	\(-6\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}+(-1+\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)