Space of modular forms of level 260 and weight 2

• Label: 260.2
• Level: 260
• Weight: 2
• Dimension: 1000
• Nonzero newspaces: 20
• Newform subspaces: 43
• Sturm bound: 8064
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 43 \)
Sturm bound:			\(8064\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(260))\).

	Total	New	Old
Modular forms	2256	1128	1128
Cusp forms	1777	1000	777
Eisenstein series	479	128	351

Trace form

1000 * q - 8 * q^2 + 4 * q^3 - 12 * q^4 - 26 * q^5 - 36 * q^6 - 20 * q^8 - 10 * q^9 - 30 * q^10 + 12 * q^11 - 24 * q^12 - 24 * q^14 + 8 * q^15 - 20 * q^16 - 18 * q^17 - 36 * q^18 - 34 * q^20 - 108 * q^21 - 72 * q^22 - 36 * q^23 - 108 * q^24 - 62 * q^25 - 100 * q^26 - 80 * q^27 - 72 * q^28 - 42 * q^29 - 66 * q^30 + 12 * q^31 - 88 * q^32 - 36 * q^33 - 60 * q^34 + 22 * q^35 - 60 * q^36 + 22 * q^37 - 24 * q^38 + 44 * q^39 - 4 * q^40 - 70 * q^41 + 24 * q^42 + 16 * q^43 + 48 * q^44 - 61 * q^45 + 84 * q^46 + 24 * q^47 + 84 * q^48 - 142 * q^49 + 52 * q^50 - 72 * q^51 + 100 * q^52 - 168 * q^53 + 72 * q^54 - 78 * q^55 + 72 * q^56 - 252 * q^57 + 68 * q^58 - 84 * q^59 + 12 * q^60 - 238 * q^61 + 12 * q^62 - 168 * q^63 - 177 * q^65 - 144 * q^66 - 108 * q^67 - 144 * q^68 - 156 * q^69 - 60 * q^70 - 96 * q^71 - 144 * q^72 - 112 * q^73 - 180 * q^74 - 142 * q^75 - 156 * q^76 - 144 * q^77 - 240 * q^78 - 40 * q^79 - 164 * q^80 - 154 * q^81 - 164 * q^82 - 96 * q^83 - 96 * q^84 - 21 * q^85 - 144 * q^86 - 96 * q^88 - 12 * q^89 - 36 * q^90 - 72 * q^92 - 12 * q^93 + 12 * q^94 - 8 * q^95 + 144 * q^96 + 32 * q^97 - 16 * q^98 + 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)

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
260.2.a	\(\chi_{260}(1, \cdot)\)	260.2.a.a	1	1
		260.2.a.b	3
260.2.c	\(\chi_{260}(209, \cdot)\)	260.2.c.a	6	1
260.2.d	\(\chi_{260}(129, \cdot)\)	260.2.d.a	8	1
260.2.f	\(\chi_{260}(181, \cdot)\)	260.2.f.a	6	1
260.2.i	\(\chi_{260}(61, \cdot)\)	260.2.i.a	2	2
		260.2.i.b	2
		260.2.i.c	2
		260.2.i.d	2
260.2.j	\(\chi_{260}(31, \cdot)\)	260.2.j.a	56	2
260.2.m	\(\chi_{260}(57, \cdot)\)	260.2.m.a	2	2
		260.2.m.b	4
		260.2.m.c	8
260.2.o	\(\chi_{260}(27, \cdot)\)	260.2.o.a	72	2
260.2.p	\(\chi_{260}(103, \cdot)\)	260.2.p.a	2	2
		260.2.p.b	2
		260.2.p.c	8
		260.2.p.d	64
260.2.r	\(\chi_{260}(177, \cdot)\)	260.2.r.a	2	2
		260.2.r.b	4
		260.2.r.c	8
260.2.u	\(\chi_{260}(99, \cdot)\)	260.2.u.a	2	2
		260.2.u.b	2
		260.2.u.c	72
260.2.x	\(\chi_{260}(101, \cdot)\)	260.2.x.a	8	2
260.2.z	\(\chi_{260}(49, \cdot)\)	260.2.z.a	16	2
260.2.ba	\(\chi_{260}(9, \cdot)\)	260.2.ba.a	12	2
260.2.bc	\(\chi_{260}(19, \cdot)\)	260.2.bc.a	4	4
		260.2.bc.b	4
		260.2.bc.c	144
260.2.bf	\(\chi_{260}(37, \cdot)\)	260.2.bf.a	4	4
		260.2.bf.b	4
		260.2.bf.c	20
260.2.bg	\(\chi_{260}(23, \cdot)\)	260.2.bg.a	4	4
		260.2.bg.b	4
		260.2.bg.c	144
260.2.bj	\(\chi_{260}(3, \cdot)\)	260.2.bj.a	4	4
		260.2.bj.b	4
		260.2.bj.c	144
260.2.bk	\(\chi_{260}(33, \cdot)\)	260.2.bk.a	4	4
		260.2.bk.b	4
		260.2.bk.c	20
260.2.bn	\(\chi_{260}(11, \cdot)\)	260.2.bn.a	112	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(260))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(260)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 1}\)