Space of modular forms of level 650 and weight 2

• Label: 650.2
• Level: 650
• Weight: 2
• Dimension: 3823
• Nonzero newspaces: 24
• Newform subspaces: 123
• Sturm bound: 50400
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 123 \)
Sturm bound:			\(50400\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(650))\).

	Total	New	Old
Modular forms	13272	3823	9449
Cusp forms	11929	3823	8106
Eisenstein series	1343	0	1343

Trace form

3823 * q + 2 * q^2 + 8 * q^3 + 2 * q^4 + 10 * q^5 + 8 * q^6 + 20 * q^7 + 5 * q^8 + 42 * q^9 + 10 * q^10 + 36 * q^11 + 12 * q^12 + 38 * q^13 + 28 * q^14 + 40 * q^15 + 6 * q^16 + 11 * q^17 - 9 * q^18 - 12 * q^19 + 12 * q^21 - 56 * q^22 - 20 * q^23 - 32 * q^24 - 70 * q^25 - 6 * q^26 - 4 * q^27 - 20 * q^28 + 19 * q^29 - 40 * q^30 + 24 * q^31 - 8 * q^32 + 76 * q^33 + 10 * q^34 + 40 * q^35 + 50 * q^36 + 97 * q^37 + 76 * q^38 + 68 * q^39 + 10 * q^40 + 95 * q^41 + 100 * q^42 + 52 * q^43 + 48 * q^44 - 30 * q^45 + 72 * q^46 + 64 * q^47 + 8 * q^48 + 56 * q^49 + 38 * q^50 - 96 * q^51 - 3 * q^52 - 138 * q^53 - 172 * q^54 - 104 * q^55 - 68 * q^56 - 416 * q^57 - 129 * q^58 - 240 * q^59 - 96 * q^60 - 149 * q^61 - 308 * q^62 - 620 * q^63 - 19 * q^64 - 227 * q^65 - 360 * q^66 - 332 * q^67 - 105 * q^68 - 640 * q^69 - 224 * q^70 - 136 * q^71 - 142 * q^72 - 212 * q^73 - 301 * q^74 - 360 * q^75 - 108 * q^76 - 296 * q^77 - 272 * q^78 - 96 * q^79 - 2 * q^80 + 14 * q^81 - 49 * q^82 - 56 * q^83 - 28 * q^84 - 30 * q^85 - 8 * q^86 + 80 * q^87 + 24 * q^88 + 66 * q^89 + 10 * q^90 + 108 * q^91 + 32 * q^92 + 248 * q^93 + 156 * q^94 + 120 * q^95 + 8 * q^96 + 256 * q^97 + 162 * q^98 + 300 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)

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
650.2.a	\(\chi_{650}(1, \cdot)\)	650.2.a.a	1	1
		650.2.a.b	1
		650.2.a.c	1
		650.2.a.d	1
		650.2.a.e	1
		650.2.a.f	1
		650.2.a.g	1
		650.2.a.h	1
		650.2.a.i	1
		650.2.a.j	1
		650.2.a.k	1
		650.2.a.l	1
		650.2.a.m	1
		650.2.a.n	3
		650.2.a.o	3
650.2.b	\(\chi_{650}(599, \cdot)\)	650.2.b.a	2	1
		650.2.b.b	2
		650.2.b.c	2
		650.2.b.d	2
		650.2.b.e	2
		650.2.b.f	2
		650.2.b.g	2
		650.2.b.h	2
		650.2.b.i	2
650.2.c	\(\chi_{650}(649, \cdot)\)	650.2.c.a	2	1
		650.2.c.b	2
		650.2.c.c	2
		650.2.c.d	2
		650.2.c.e	6
		650.2.c.f	6
650.2.d	\(\chi_{650}(51, \cdot)\)	650.2.d.a	2	1
		650.2.d.b	2
		650.2.d.c	6
		650.2.d.d	6
		650.2.d.e	8
650.2.e	\(\chi_{650}(451, \cdot)\)	650.2.e.a	2	2
		650.2.e.b	2
		650.2.e.c	2
		650.2.e.d	4
		650.2.e.e	4
		650.2.e.f	4
		650.2.e.g	4
		650.2.e.h	4
		650.2.e.i	4
		650.2.e.j	6
		650.2.e.k	6
650.2.g	\(\chi_{650}(57, \cdot)\)	650.2.g.a	2	2
		650.2.g.b	2
		650.2.g.c	2
		650.2.g.d	2
		650.2.g.e	2
		650.2.g.f	4
		650.2.g.g	4
		650.2.g.h	12
		650.2.g.i	12
650.2.j	\(\chi_{650}(307, \cdot)\)	650.2.j.a	2	2
		650.2.j.b	2
		650.2.j.c	2
		650.2.j.d	2
		650.2.j.e	2
		650.2.j.f	4
		650.2.j.g	4
		650.2.j.h	12
		650.2.j.i	12
650.2.l	\(\chi_{650}(131, \cdot)\)	650.2.l.a	4	4
		650.2.l.b	20
		650.2.l.c	24
		650.2.l.d	36
		650.2.l.e	36
650.2.m	\(\chi_{650}(101, \cdot)\)	650.2.m.a	4	2
		650.2.m.b	8
		650.2.m.c	8
		650.2.m.d	8
		650.2.m.e	16
650.2.n	\(\chi_{650}(49, \cdot)\)	650.2.n.a	4	2
		650.2.n.b	4
		650.2.n.c	8
		650.2.n.d	8
		650.2.n.e	8
		650.2.n.f	8
650.2.o	\(\chi_{650}(399, \cdot)\)	650.2.o.a	4	2
		650.2.o.b	4
		650.2.o.c	4
		650.2.o.d	4
		650.2.o.e	4
		650.2.o.f	8
		650.2.o.g	8
		650.2.o.h	8
650.2.p	\(\chi_{650}(181, \cdot)\)	650.2.p.a	136	4
650.2.q	\(\chi_{650}(79, \cdot)\)	650.2.q.a	48	4
		650.2.q.b	72
650.2.r	\(\chi_{650}(129, \cdot)\)	650.2.r.a	72	4
		650.2.r.b	72
650.2.t	\(\chi_{650}(7, \cdot)\)	650.2.t.a	4	4
		650.2.t.b	4
		650.2.t.c	8
		650.2.t.d	8
		650.2.t.e	12
		650.2.t.f	16
		650.2.t.g	16
		650.2.t.h	16
650.2.w	\(\chi_{650}(193, \cdot)\)	650.2.w.a	4	4
		650.2.w.b	4
		650.2.w.c	8
		650.2.w.d	8
		650.2.w.e	12
		650.2.w.f	16
		650.2.w.g	16
		650.2.w.h	16
650.2.y	\(\chi_{650}(61, \cdot)\)	650.2.y.a	136	8
		650.2.y.b	152
650.2.ba	\(\chi_{650}(73, \cdot)\)	650.2.ba.a	136	8
		650.2.ba.b	144
650.2.bd	\(\chi_{650}(47, \cdot)\)	650.2.bd.a	136	8
		650.2.bd.b	144
650.2.bf	\(\chi_{650}(69, \cdot)\)	650.2.bf.a	144	8
		650.2.bf.b	144
650.2.bg	\(\chi_{650}(9, \cdot)\)	650.2.bg.a	272	8
650.2.bh	\(\chi_{650}(121, \cdot)\)	650.2.bh.a	272	8
650.2.bj	\(\chi_{650}(37, \cdot)\)	650.2.bj.a	272	16
		650.2.bj.b	288
650.2.bm	\(\chi_{650}(33, \cdot)\)	650.2.bm.a	272	16
		650.2.bm.b	288

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(650))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(650)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 1}\)