Space of modular forms of level 847 and weight 2

• Label: 847.2
• Level: 847
• Weight: 2
• Dimension: 26671
• Nonzero newspaces: 16
• Newform subspaces: 106
• Sturm bound: 116160
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 106 \)
Sturm bound:			\(116160\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(847))\).

	Total	New	Old
Modular forms	30000	28075	1925
Cusp forms	28081	26671	1410
Eisenstein series	1919	1404	515

Trace form

26671 * q - 177 * q^2 - 176 * q^3 - 173 * q^4 - 174 * q^5 - 188 * q^6 - 234 * q^7 - 475 * q^8 - 207 * q^9 - 222 * q^10 - 210 * q^11 - 392 * q^12 - 186 * q^13 - 252 * q^14 - 506 * q^15 - 269 * q^16 - 222 * q^17 - 261 * q^18 - 220 * q^19 - 278 * q^20 - 271 * q^21 - 560 * q^22 - 376 * q^23 - 340 * q^24 - 269 * q^25 - 318 * q^26 - 260 * q^27 - 328 * q^28 - 520 * q^29 - 368 * q^30 - 228 * q^31 - 317 * q^32 - 280 * q^33 - 446 * q^34 - 309 * q^35 - 719 * q^36 - 262 * q^37 - 340 * q^38 - 344 * q^39 - 430 * q^40 - 318 * q^41 - 403 * q^42 - 586 * q^43 - 340 * q^44 - 542 * q^45 - 368 * q^46 - 272 * q^47 - 516 * q^48 - 334 * q^49 - 677 * q^50 - 368 * q^51 - 422 * q^52 - 346 * q^53 - 560 * q^54 - 320 * q^55 - 630 * q^56 - 670 * q^57 - 430 * q^58 - 320 * q^59 - 312 * q^60 - 238 * q^61 - 384 * q^62 - 222 * q^63 - 603 * q^64 - 216 * q^65 - 210 * q^66 - 412 * q^67 - 194 * q^68 - 144 * q^69 - 117 * q^70 - 418 * q^71 - 25 * q^72 - 186 * q^73 - 286 * q^74 - 36 * q^75 + 80 * q^76 - 245 * q^77 - 802 * q^78 - 260 * q^79 - 134 * q^80 - 39 * q^81 - 234 * q^82 - 256 * q^83 + 93 * q^84 - 522 * q^85 - 148 * q^86 - 220 * q^87 - 340 * q^88 - 390 * q^89 - 366 * q^90 - 261 * q^91 - 702 * q^92 - 392 * q^93 - 536 * q^94 - 460 * q^95 - 468 * q^96 - 482 * q^97 - 472 * q^98 - 780 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)

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
847.2.a	\(\chi_{847}(1, \cdot)\)	847.2.a.a	1	1
		847.2.a.b	1
		847.2.a.c	1
		847.2.a.d	2
		847.2.a.e	2
		847.2.a.f	2
		847.2.a.g	2
		847.2.a.h	2
		847.2.a.i	3
		847.2.a.j	3
		847.2.a.k	4
		847.2.a.l	4
		847.2.a.m	6
		847.2.a.n	6
		847.2.a.o	8
		847.2.a.p	8
847.2.b	\(\chi_{847}(846, \cdot)\)	847.2.b.a	8	1
		847.2.b.b	8
		847.2.b.c	8
		847.2.b.d	8
		847.2.b.e	16
		847.2.b.f	16
847.2.e	\(\chi_{847}(485, \cdot)\)	847.2.e.a	4	2
		847.2.e.b	4
		847.2.e.c	6
		847.2.e.d	6
		847.2.e.e	12
		847.2.e.f	14
		847.2.e.g	14
		847.2.e.h	20
		847.2.e.i	20
		847.2.e.j	28
847.2.f	\(\chi_{847}(148, \cdot)\)	847.2.f.a	4	4
		847.2.f.b	4
		847.2.f.c	4
		847.2.f.d	4
		847.2.f.e	4
		847.2.f.f	4
		847.2.f.g	4
		847.2.f.h	4
		847.2.f.i	4
		847.2.f.j	4
		847.2.f.k	4
		847.2.f.l	4
		847.2.f.m	4
		847.2.f.n	4
		847.2.f.o	8
		847.2.f.p	8
		847.2.f.q	8
		847.2.f.r	8
		847.2.f.s	8
		847.2.f.t	12
		847.2.f.u	12
		847.2.f.v	16
		847.2.f.w	16
		847.2.f.x	16
		847.2.f.y	24
		847.2.f.z	24
847.2.i	\(\chi_{847}(241, \cdot)\)	847.2.i.a	24	2
		847.2.i.b	48
		847.2.i.c	56
847.2.l	\(\chi_{847}(118, \cdot)\)	847.2.l.a	8	4
		847.2.l.b	8
		847.2.l.c	8
		847.2.l.d	8
		847.2.l.e	16
		847.2.l.f	16
		847.2.l.g	16
		847.2.l.h	16
		847.2.l.i	16
		847.2.l.j	16
		847.2.l.k	32
		847.2.l.l	32
		847.2.l.m	64
847.2.m	\(\chi_{847}(78, \cdot)\)	847.2.m.a	320	10
		847.2.m.b	340
847.2.n	\(\chi_{847}(9, \cdot)\)	847.2.n.a	8	8
		847.2.n.b	8
		847.2.n.c	8
		847.2.n.d	24
		847.2.n.e	24
		847.2.n.f	24
		847.2.n.g	24
		847.2.n.h	40
		847.2.n.i	40
		847.2.n.j	40
		847.2.n.k	48
		847.2.n.l	56
		847.2.n.m	56
		847.2.n.n	112
847.2.p	\(\chi_{847}(76, \cdot)\)	847.2.p.a	20	10
		847.2.p.b	840
847.2.r	\(\chi_{847}(40, \cdot)\)	847.2.r.a	48	8
		847.2.r.b	48
		847.2.r.c	48
		847.2.r.d	48
		847.2.r.e	96
		847.2.r.f	224
847.2.u	\(\chi_{847}(23, \cdot)\)	847.2.u.a	1720	20
847.2.v	\(\chi_{847}(15, \cdot)\)	847.2.v.a	1280	40
		847.2.v.b	1360
847.2.x	\(\chi_{847}(10, \cdot)\)	847.2.x.a	1720	20
847.2.ba	\(\chi_{847}(6, \cdot)\)	847.2.ba.a	80	40
		847.2.ba.b	3360
847.2.bc	\(\chi_{847}(4, \cdot)\)	847.2.bc.a	6880	80
847.2.be	\(\chi_{847}(17, \cdot)\)	847.2.be.a	6880	80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(847))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(847)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)