Space of modular forms of level 266 and weight 2

• Label: 266.2
• Level: 266
• Weight: 2
• Dimension: 689
• Nonzero newspaces: 16
• Newform subspaces: 37
• Sturm bound: 8640
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 266 = 2 \cdot 7 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 37 \)
Sturm bound:			\(8640\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(266))\).

	Total	New	Old
Modular forms	2376	689	1687
Cusp forms	1945	689	1256
Eisenstein series	431	0	431

Trace form

689 * q + 3 * q^2 + 8 * q^3 - q^4 + 6 * q^5 - q^7 + 3 * q^8 + 11 * q^9 + 6 * q^10 + 12 * q^11 - 4 * q^12 - 26 * q^13 - 15 * q^14 - 48 * q^15 - q^16 - 30 * q^17 - 39 * q^18 - 67 * q^19 - 30 * q^20 - 34 * q^21 - 42 * q^22 - 12 * q^23 - 31 * q^25 - 30 * q^26 - 34 * q^27 - 7 * q^28 + 6 * q^29 + 24 * q^30 + 4 * q^31 + 3 * q^32 - 60 * q^33 + 30 * q^34 - 30 * q^35 + 11 * q^36 - 2 * q^37 + 21 * q^38 - 68 * q^39 + 6 * q^40 - 6 * q^41 - 56 * q^43 - 6 * q^44 - 138 * q^45 - 48 * q^46 - 72 * q^47 - 10 * q^48 - 19 * q^49 - 123 * q^50 - 102 * q^51 + 10 * q^52 - 102 * q^53 - 60 * q^54 - 72 * q^55 - 33 * q^56 - 100 * q^57 - 54 * q^58 - 108 * q^59 - 48 * q^60 - 110 * q^61 - 84 * q^62 - 85 * q^63 - 13 * q^64 - 132 * q^65 - 96 * q^66 - 80 * q^67 - 12 * q^68 - 12 * q^69 - 30 * q^70 - 72 * q^71 - 3 * q^72 + 4 * q^73 + 42 * q^74 + 20 * q^75 + 17 * q^76 - 24 * q^77 - 92 * q^79 + 6 * q^80 - 55 * q^81 - 18 * q^82 - 48 * q^83 - 46 * q^84 - 36 * q^85 - 12 * q^86 - 264 * q^87 + 12 * q^88 - 42 * q^89 - 102 * q^90 - 74 * q^91 - 48 * q^92 - 188 * q^93 - 120 * q^94 - 66 * q^95 - 62 * q^97 - 69 * q^98 - 258 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)

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
266.2.a	\(\chi_{266}(1, \cdot)\)	266.2.a.a	2	1
		266.2.a.b	2
		266.2.a.c	2
		266.2.a.d	3
266.2.d	\(\chi_{266}(265, \cdot)\)	266.2.d.a	16	1
266.2.e	\(\chi_{266}(39, \cdot)\)	266.2.e.a	2	2
		266.2.e.b	2
		266.2.e.c	4
		266.2.e.d	6
		266.2.e.e	10
266.2.f	\(\chi_{266}(197, \cdot)\)	266.2.f.a	2	2
		266.2.f.b	4
		266.2.f.c	6
		266.2.f.d	8
266.2.g	\(\chi_{266}(11, \cdot)\)	266.2.g.a	2	2
		266.2.g.b	10
		266.2.g.c	12
266.2.h	\(\chi_{266}(163, \cdot)\)	266.2.h.a	2	2
		266.2.h.b	10
		266.2.h.c	12
266.2.k	\(\chi_{266}(145, \cdot)\)	266.2.k.a	4	2
		266.2.k.b	20
266.2.l	\(\chi_{266}(75, \cdot)\)	266.2.l.a	24	2
266.2.m	\(\chi_{266}(27, \cdot)\)	266.2.m.a	32	2
266.2.t	\(\chi_{266}(31, \cdot)\)	266.2.t.a	4	2
		266.2.t.b	20
266.2.u	\(\chi_{266}(43, \cdot)\)	266.2.u.a	6	6
		266.2.u.b	12
		266.2.u.c	18
		266.2.u.d	24
266.2.v	\(\chi_{266}(9, \cdot)\)	266.2.v.a	42	6
		266.2.v.b	42
266.2.w	\(\chi_{266}(25, \cdot)\)	266.2.w.a	42	6
		266.2.w.b	42
266.2.x	\(\chi_{266}(13, \cdot)\)	266.2.x.a	72	6
266.2.y	\(\chi_{266}(3, \cdot)\)	266.2.y.a	84	6
266.2.bd	\(\chi_{266}(33, \cdot)\)	266.2.bd.a	84	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(266))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(266)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 2}\)