Space of modular forms of level 875 and weight 2

• Label: 875.2
• Level: 875
• Weight: 2
• Dimension: 25856
• Nonzero newspaces: 18
• Newform subspaces: 57
• Sturm bound: 120000
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 57 \)
Sturm bound:			\(120000\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(875))\).

	Total	New	Old
Modular forms	31080	27136	3944
Cusp forms	28921	25856	3065
Eisenstein series	2159	1280	879

Trace form

25856 * q - 126 * q^2 - 124 * q^3 - 118 * q^4 - 160 * q^5 - 216 * q^6 - 154 * q^7 - 294 * q^8 - 106 * q^9 - 160 * q^10 - 216 * q^11 - 76 * q^12 - 104 * q^13 - 138 * q^14 - 400 * q^15 - 242 * q^16 - 136 * q^17 - 154 * q^18 - 172 * q^19 - 230 * q^20 - 302 * q^21 - 412 * q^22 - 164 * q^23 - 340 * q^24 - 220 * q^25 - 340 * q^26 - 208 * q^27 - 274 * q^28 - 368 * q^29 - 240 * q^30 - 280 * q^31 - 218 * q^32 - 176 * q^33 - 184 * q^34 - 210 * q^35 - 726 * q^36 - 112 * q^37 - 180 * q^38 - 240 * q^39 - 260 * q^40 - 260 * q^41 - 338 * q^42 - 420 * q^43 - 292 * q^44 - 320 * q^45 - 360 * q^46 - 208 * q^47 - 556 * q^48 - 152 * q^49 - 580 * q^50 - 416 * q^51 - 424 * q^52 - 204 * q^53 - 484 * q^54 - 240 * q^55 - 406 * q^56 - 532 * q^57 - 328 * q^58 - 260 * q^59 - 440 * q^60 - 348 * q^61 - 488 * q^62 - 334 * q^63 - 654 * q^64 - 270 * q^65 - 528 * q^66 - 252 * q^67 - 516 * q^68 - 328 * q^69 - 280 * q^70 - 652 * q^71 - 626 * q^72 - 240 * q^73 - 476 * q^74 - 320 * q^75 - 632 * q^76 - 298 * q^77 - 652 * q^78 - 228 * q^79 - 440 * q^80 - 374 * q^81 - 480 * q^82 - 452 * q^83 - 506 * q^84 - 630 * q^85 - 528 * q^86 - 472 * q^87 - 740 * q^88 - 512 * q^89 - 580 * q^90 - 430 * q^91 - 692 * q^92 - 480 * q^93 - 580 * q^94 - 320 * q^95 - 464 * q^96 - 568 * q^97 - 476 * q^98 - 628 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(875))\)

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
875.2.a	\(\chi_{875}(1, \cdot)\)	875.2.a.a	2	1
		875.2.a.b	2
		875.2.a.c	2
		875.2.a.d	2
		875.2.a.e	6
		875.2.a.f	6
		875.2.a.g	6
		875.2.a.h	6
		875.2.a.i	8
		875.2.a.j	8
875.2.b	\(\chi_{875}(624, \cdot)\)	875.2.b.a	4	1
		875.2.b.b	4
		875.2.b.c	12
		875.2.b.d	12
		875.2.b.e	16
875.2.e	\(\chi_{875}(501, \cdot)\)	875.2.e.a	4	2
		875.2.e.b	4
		875.2.e.c	24
		875.2.e.d	28
		875.2.e.e	28
		875.2.e.f	40
875.2.f	\(\chi_{875}(307, \cdot)\)	875.2.f.a	16	2
		875.2.f.b	16
		875.2.f.c	32
		875.2.f.d	64
875.2.h	\(\chi_{875}(176, \cdot)\)	875.2.h.a	4	4
		875.2.h.b	28
		875.2.h.c	32
		875.2.h.d	56
		875.2.h.e	56
875.2.k	\(\chi_{875}(249, \cdot)\)	875.2.k.a	8	2
		875.2.k.b	24
		875.2.k.c	40
		875.2.k.d	56
875.2.n	\(\chi_{875}(99, \cdot)\)	875.2.n.a	8	4
		875.2.n.b	56
		875.2.n.c	56
		875.2.n.d	64
875.2.o	\(\chi_{875}(68, \cdot)\)	875.2.o.a	128	4
		875.2.o.b	128
875.2.q	\(\chi_{875}(51, \cdot)\)	875.2.q.a	144	8
		875.2.q.b	288
875.2.s	\(\chi_{875}(118, \cdot)\)	875.2.s.a	144	8
		875.2.s.b	144
		875.2.s.c	144
875.2.t	\(\chi_{875}(36, \cdot)\)	875.2.t.a	760	20
		875.2.t.b	760
875.2.u	\(\chi_{875}(74, \cdot)\)	875.2.u.a	144	8
		875.2.u.b	288
875.2.y	\(\chi_{875}(29, \cdot)\)	875.2.y.a	1480	20
875.2.bb	\(\chi_{875}(82, \cdot)\)	875.2.bb.a	288	16
		875.2.bb.b	288
		875.2.bb.c	288
875.2.bc	\(\chi_{875}(11, \cdot)\)	875.2.bc.a	3920	40
875.2.bd	\(\chi_{875}(13, \cdot)\)	875.2.bd.a	3920	40
875.2.bg	\(\chi_{875}(4, \cdot)\)	875.2.bg.a	3920	40
875.2.bj	\(\chi_{875}(3, \cdot)\)	875.2.bj.a	7840	80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(875))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(875)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)