Space of modular forms of level 850 and weight 2

• Label: 850.2
• Level: 850
• Weight: 2
• Dimension: 6588
• Nonzero newspaces: 20
• Newform subspaces: 129
• Sturm bound: 86400
• Trace bound: 27

Defining parameters

Level:	\( N \)	=	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 129 \)
Sturm bound:			\(86400\)
Trace bound:			\(27\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(850))\).

	Total	New	Old
Modular forms	22496	6588	15908
Cusp forms	20705	6588	14117
Eisenstein series	1791	0	1791

Trace form

6588 * q + 2 * q^2 + 8 * q^3 + 2 * q^4 + 10 * q^5 + 8 * q^6 + 16 * q^7 + 2 * q^8 + 26 * q^9 + 10 * q^10 + 40 * q^11 + 16 * q^12 + 44 * q^13 + 32 * q^14 + 40 * q^15 + 6 * q^16 + 14 * q^17 + 8 * q^18 - 24 * q^19 + 32 * q^21 - 40 * q^22 - 16 * q^23 - 24 * q^24 - 70 * q^25 - 8 * q^26 - 16 * q^27 - 24 * q^28 - 40 * q^30 + 16 * q^31 - 8 * q^32 + 48 * q^33 - 7 * q^34 + 40 * q^35 + 26 * q^36 + 98 * q^37 + 48 * q^38 + 96 * q^39 + 10 * q^40 + 112 * q^41 + 112 * q^42 + 64 * q^43 + 56 * q^44 - 30 * q^45 + 80 * q^46 + 96 * q^47 + 8 * q^48 + 88 * q^49 + 50 * q^50 + 76 * q^51 + 60 * q^52 + 86 * q^53 + 136 * q^54 + 40 * q^55 + 16 * q^56 + 88 * q^57 + 92 * q^58 + 80 * q^59 + 52 * q^61 - 8 * q^62 + 24 * q^63 + 2 * q^64 - 70 * q^65 - 16 * q^66 - 8 * q^67 - 70 * q^68 - 280 * q^69 - 208 * q^70 - 224 * q^71 - 114 * q^72 - 568 * q^73 - 376 * q^74 - 376 * q^75 - 40 * q^76 - 560 * q^77 - 536 * q^78 - 432 * q^79 - 54 * q^80 - 582 * q^81 - 552 * q^82 - 464 * q^83 - 280 * q^84 - 399 * q^85 - 256 * q^86 - 664 * q^87 - 200 * q^88 - 318 * q^89 - 262 * q^90 - 544 * q^91 - 104 * q^92 - 248 * q^93 - 352 * q^94 - 136 * q^95 + 8 * q^96 - 260 * q^97 - 138 * q^98 - 264 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(850))\)

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
850.2.a	\(\chi_{850}(1, \cdot)\)	850.2.a.a	1	1
		850.2.a.b	1
		850.2.a.c	1
		850.2.a.d	1
		850.2.a.e	1
		850.2.a.f	1
		850.2.a.g	1
		850.2.a.h	1
		850.2.a.i	1
		850.2.a.j	1
		850.2.a.k	1
		850.2.a.l	1
		850.2.a.m	2
		850.2.a.n	2
		850.2.a.o	2
		850.2.a.p	3
		850.2.a.q	3
850.2.b	\(\chi_{850}(101, \cdot)\)	850.2.b.a	2	1
		850.2.b.b	2
		850.2.b.c	2
		850.2.b.d	2
		850.2.b.e	2
		850.2.b.f	2
		850.2.b.g	2
		850.2.b.h	2
		850.2.b.i	2
		850.2.b.j	2
		850.2.b.k	4
		850.2.b.l	4
850.2.c	\(\chi_{850}(749, \cdot)\)	850.2.c.a	2	1
		850.2.c.b	2
		850.2.c.c	2
		850.2.c.d	2
		850.2.c.e	2
		850.2.c.f	2
		850.2.c.g	2
		850.2.c.h	2
		850.2.c.i	4
		850.2.c.j	4
850.2.d	\(\chi_{850}(849, \cdot)\)	850.2.d.a	2	1
		850.2.d.b	2
		850.2.d.c	2
		850.2.d.d	2
		850.2.d.e	2
		850.2.d.f	2
		850.2.d.g	2
		850.2.d.h	2
		850.2.d.i	4
		850.2.d.j	8
850.2.g	\(\chi_{850}(149, \cdot)\)	850.2.g.a	2	2
		850.2.g.b	2
		850.2.g.c	2
		850.2.g.d	2
		850.2.g.e	4
		850.2.g.f	4
		850.2.g.g	4
		850.2.g.h	4
		850.2.g.i	8
		850.2.g.j	8
		850.2.g.k	8
		850.2.g.l	8
850.2.h	\(\chi_{850}(251, \cdot)\)	850.2.h.a	2	2
		850.2.h.b	2
		850.2.h.c	2
		850.2.h.d	2
		850.2.h.e	2
		850.2.h.f	2
		850.2.h.g	4
		850.2.h.h	4
		850.2.h.i	4
		850.2.h.j	4
		850.2.h.k	4
		850.2.h.l	8
		850.2.h.m	8
		850.2.h.n	8
850.2.k	\(\chi_{850}(171, \cdot)\)	850.2.k.a	4	4
		850.2.k.b	4
		850.2.k.c	32
		850.2.k.d	36
		850.2.k.e	40
		850.2.k.f	44
850.2.l	\(\chi_{850}(151, \cdot)\)	850.2.l.a	4	4
		850.2.l.b	8
		850.2.l.c	8
		850.2.l.d	8
		850.2.l.e	16
		850.2.l.f	16
		850.2.l.g	16
		850.2.l.h	20
		850.2.l.i	20
850.2.o	\(\chi_{850}(49, \cdot)\)	850.2.o.a	4	4
		850.2.o.b	4
		850.2.o.c	8
		850.2.o.d	8
		850.2.o.e	8
		850.2.o.f	8
		850.2.o.g	16
		850.2.o.h	16
		850.2.o.i	16
		850.2.o.j	16
850.2.p	\(\chi_{850}(169, \cdot)\)	850.2.p.a	176	4
850.2.q	\(\chi_{850}(69, \cdot)\)	850.2.q.a	72	4
		850.2.q.b	88
850.2.r	\(\chi_{850}(271, \cdot)\)	850.2.r.a	88	4
		850.2.r.b	96
850.2.s	\(\chi_{850}(7, \cdot)\)	850.2.s.a	24	8
		850.2.s.b	24
		850.2.s.c	32
		850.2.s.d	40
		850.2.s.e	48
		850.2.s.f	48
850.2.v	\(\chi_{850}(107, \cdot)\)	850.2.v.a	24	8
		850.2.v.b	24
		850.2.v.c	32
		850.2.v.d	40
		850.2.v.e	48
		850.2.v.f	48
850.2.y	\(\chi_{850}(21, \cdot)\)	850.2.y.a	176	8
		850.2.y.b	192
850.2.z	\(\chi_{850}(89, \cdot)\)	850.2.z.a	176	8
		850.2.z.b	176
850.2.bc	\(\chi_{850}(9, \cdot)\)	850.2.bc.a	368	16
		850.2.bc.b	368
850.2.bf	\(\chi_{850}(111, \cdot)\)	850.2.bf.a	352	16
		850.2.bf.b	352
850.2.bg	\(\chi_{850}(23, \cdot)\)	850.2.bg.a	704	32
		850.2.bg.b	736
850.2.bj	\(\chi_{850}(3, \cdot)\)	850.2.bj.a	704	32
		850.2.bj.b	736

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(850))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(850)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 2}\)