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

• Label: 65.2.o
• Level: $65$
• Weight: $2$
• Character orbit: 65.o
• Rep. character: $\chi_{65}(2,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $14$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$65 = 5 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	65.o (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$65$
Character field:			$\Q(\zeta_{12})$
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	36	36	0
Cusp forms	20	20	0
Eisenstein series	16	16	0

Trace form

20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * 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.o.a	$65$	$2$	65.o	65.o	$12$	$20$	$5$	$0.519$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓	✓	65.2.o.a	$2$	$0$	$-4$	$-2$	$-6$	$-6$	$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{3}+\beta _{4})q^{2}+(\beta _{2}+\beta _{4}+\beta _{8}-\beta _{12}+\cdots)q^{3}+\cdots$