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

• Label: 65.2.e
• Level: $65$
• Weight: $2$
• Character orbit: 65.e
• Rep. character: $\chi_{65}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $14$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(14\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	16	8	8
Cusp forms	8	8	0
Eisenstein series	8	0	8

Trace form

8 * q - 2 * q^3 - 2 * q^4 + 6 * q^6 - 2 * q^7 - 12 * q^8 - 2 * q^10 - 4 * q^12 - 4 * q^13 - 4 * q^14 + 2 * q^15 + 6 * q^16 - 10 * q^17 + 8 * q^18 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 6 * q^23 - 4 * q^24 + 8 * q^25 - 6 * q^26 - 20 * q^27 + 10 * q^28 + 4 * q^29 + 4 * q^30 - 16 * q^31 + 2 * q^32 + 14 * q^33 - 12 * q^34 - 6 * q^35 + 8 * q^36 - 6 * q^37 + 24 * q^38 + 12 * q^40 - 12 * q^41 + 4 * q^42 + 14 * q^43 + 20 * q^44 - 8 * q^45 - 14 * q^46 + 24 * q^47 - 12 * q^48 + 8 * q^49 - 24 * q^51 + 18 * q^52 + 40 * q^53 - 10 * q^54 - 8 * q^55 - 16 * q^56 + 12 * q^57 - 32 * q^58 - 12 * q^59 - 16 * q^60 - 4 * q^62 - 12 * q^63 - 4 * q^65 - 52 * q^66 + 6 * q^67 - 34 * q^68 + 16 * q^69 - 8 * q^70 + 20 * q^71 - 12 * q^72 - 56 * q^73 + 10 * q^74 - 2 * q^75 + 26 * q^76 + 4 * q^77 + 12 * q^78 - 8 * q^79 + 20 * q^81 + 20 * q^82 - 8 * q^83 + 18 * q^84 + 6 * q^85 + 60 * q^86 + 18 * q^87 - 2 * q^88 + 16 * q^89 - 20 * q^91 - 20 * q^92 + 8 * q^93 + 4 * q^94 - 8 * q^95 + 4 * q^96 + 22 * q^97 + 12 * q^98 + 32 * 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.e.a	$65$	$2$	65.e	13.c	$3$	$4$	$2$	$0.519$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		✓			65.2.e.a	$2$	$0$	\(-1\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-1+2\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
65.2.e.b	$65$	$2$	65.e	13.c	$3$	$4$	$2$	$0.519$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		✓			65.2.e.b	$2$	$0$	\(1\)	\(-2\)	\(-4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)