Space of modular forms of level 65 and weight 2

• Label: 65.2
• Level: 65
• Weight: 2
• Dimension: 117
• Nonzero newspaces: 12
• Newform subspaces: 18
• Sturm bound: 672
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(672\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(65))\).

	Total	New	Old
Modular forms	216	185	31
Cusp forms	121	117	4
Eisenstein series	95	68	27

Trace form

117 * q - 15 * q^2 - 16 * q^3 - 19 * q^4 - 19 * q^5 - 48 * q^6 - 16 * q^7 - 9 * q^8 - 9 * q^9 - 6 * q^10 - 36 * q^11 + 12 * q^12 - q^13 - 24 * q^14 - 10 * q^15 - 27 * q^16 - 12 * q^17 + 15 * q^18 + 8 * q^19 + 8 * q^20 - 16 * q^21 + 12 * q^22 - 12 * q^23 + 48 * q^24 - 13 * q^25 - 15 * q^26 + 8 * q^27 + 32 * q^28 + 12 * q^29 + 42 * q^30 - 16 * q^31 + 57 * q^32 + 24 * q^33 + 30 * q^34 + 16 * q^35 + 41 * q^36 - 16 * q^37 + 12 * q^38 + 21 * q^40 + 12 * q^41 + 72 * q^42 + 36 * q^43 + 60 * q^44 + 44 * q^45 + 60 * q^46 + 24 * q^47 - 16 * q^48 + 47 * q^49 + 60 * q^50 - 21 * q^52 - 30 * q^53 - 72 * q^54 - 36 * q^55 - 72 * q^56 - 64 * q^57 - 60 * q^58 - 60 * q^59 - 172 * q^60 - 32 * q^61 - 84 * q^62 - 88 * q^63 - 97 * q^64 - 46 * q^65 - 144 * q^66 - 64 * q^67 - 72 * q^68 - 120 * q^69 - 48 * q^70 - 36 * q^71 - 123 * q^72 - 22 * q^73 + 12 * q^74 - 30 * q^75 - 40 * q^76 + 36 * q^78 - 32 * q^79 + 62 * q^80 + 3 * q^81 + 72 * q^82 + 60 * q^83 + 56 * q^84 + 57 * q^85 + 84 * q^86 + 108 * q^87 + 156 * q^88 + 90 * q^89 + 165 * q^90 + 56 * q^91 + 96 * q^92 + 128 * q^93 + 132 * q^94 + 70 * q^95 + 204 * q^96 + 50 * q^97 + 105 * q^98 + 132 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
65.2.a	\(\chi_{65}(1, \cdot)\)	65.2.a.a	1	1
		65.2.a.b	2
		65.2.a.c	2
65.2.b	\(\chi_{65}(14, \cdot)\)	65.2.b.a	6	1
65.2.c	\(\chi_{65}(51, \cdot)\)	65.2.c.a	6	1
65.2.d	\(\chi_{65}(64, \cdot)\)	65.2.d.a	2	1
		65.2.d.b	2
65.2.e	\(\chi_{65}(16, \cdot)\)	65.2.e.a	4	2
		65.2.e.b	4
65.2.f	\(\chi_{65}(18, \cdot)\)	65.2.f.a	2	2
		65.2.f.b	8
65.2.k	\(\chi_{65}(8, \cdot)\)	65.2.k.a	2	2
		65.2.k.b	8
65.2.l	\(\chi_{65}(4, \cdot)\)	65.2.l.a	8	2
65.2.m	\(\chi_{65}(36, \cdot)\)	65.2.m.a	8	2
65.2.n	\(\chi_{65}(9, \cdot)\)	65.2.n.a	12	2
65.2.o	\(\chi_{65}(2, \cdot)\)	65.2.o.a	20	4
65.2.t	\(\chi_{65}(7, \cdot)\)	65.2.t.a	20	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(65))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(65)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)