Space of modular forms of level 931 and weight 2

• Label: 931.2
• Level: 931
• Weight: 2
• Dimension: 32844
• Nonzero newspaces: 32
• Newform subspaces: 154
• Sturm bound: 141120
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Newform subspaces:			\( 154 \)
Sturm bound:			\(141120\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(931))\).

	Total	New	Old
Modular forms	36360	34492	1868
Cusp forms	34201	32844	1357
Eisenstein series	2159	1648	511

Trace form

32844 * q - 243 * q^2 - 245 * q^3 - 251 * q^4 - 249 * q^5 - 261 * q^6 - 296 * q^7 - 447 * q^8 - 263 * q^9 - 273 * q^10 - 261 * q^11 - 305 * q^12 - 277 * q^13 - 324 * q^14 - 483 * q^15 - 335 * q^16 - 282 * q^17 - 351 * q^18 - 299 * q^19 - 636 * q^20 - 338 * q^21 - 516 * q^22 - 294 * q^23 - 393 * q^24 - 317 * q^25 - 339 * q^26 - 338 * q^27 - 380 * q^28 - 495 * q^29 - 444 * q^30 - 319 * q^31 - 408 * q^32 - 387 * q^33 - 390 * q^34 - 366 * q^35 - 599 * q^36 - 284 * q^37 - 339 * q^38 - 584 * q^39 - 246 * q^40 - 255 * q^41 - 282 * q^42 - 460 * q^43 - 225 * q^44 - 264 * q^45 - 210 * q^46 - 294 * q^47 - 261 * q^48 - 212 * q^49 - 870 * q^50 - 267 * q^51 - 191 * q^52 - 297 * q^53 - 306 * q^54 - 207 * q^55 - 240 * q^56 - 539 * q^57 - 564 * q^58 - 318 * q^59 - 474 * q^60 - 329 * q^61 - 444 * q^62 - 408 * q^63 - 665 * q^64 - 504 * q^65 - 669 * q^66 - 466 * q^67 - 615 * q^68 - 528 * q^69 - 534 * q^70 - 624 * q^71 - 825 * q^72 - 469 * q^73 - 555 * q^74 - 578 * q^75 - 488 * q^76 - 774 * q^77 - 681 * q^78 - 499 * q^79 - 645 * q^80 - 428 * q^81 - 450 * q^82 - 300 * q^83 - 212 * q^84 - 573 * q^85 - 306 * q^86 - 285 * q^87 - 297 * q^88 - 330 * q^89 - 114 * q^90 - 310 * q^91 - 576 * q^92 - 91 * q^93 - 264 * q^94 - 273 * q^95 - 438 * q^96 - 286 * q^97 + 12 * q^98 - 864 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(931))\)

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
931.2.a	\(\chi_{931}(1, \cdot)\)	931.2.a.a	1	1
		931.2.a.b	1
		931.2.a.c	1
		931.2.a.d	2
		931.2.a.e	2
		931.2.a.f	2
		931.2.a.g	2
		931.2.a.h	2
		931.2.a.i	2
		931.2.a.j	2
		931.2.a.k	3
		931.2.a.l	4
		931.2.a.m	4
		931.2.a.n	7
		931.2.a.o	7
		931.2.a.p	10
		931.2.a.q	10
931.2.c	\(\chi_{931}(930, \cdot)\)	931.2.c.a	4	1
		931.2.c.b	4
		931.2.c.c	4
		931.2.c.d	6
		931.2.c.e	6
		931.2.c.f	40
931.2.e	\(\chi_{931}(197, \cdot)\)	931.2.e.a	4	2
		931.2.e.b	6
		931.2.e.c	10
		931.2.e.d	20
		931.2.e.e	24
		931.2.e.f	24
		931.2.e.g	40
931.2.f	\(\chi_{931}(324, \cdot)\)	931.2.f.a	2	2
		931.2.f.b	2
		931.2.f.c	2
		931.2.f.d	4
		931.2.f.e	4
		931.2.f.f	4
		931.2.f.g	4
		931.2.f.h	4
		931.2.f.i	4
		931.2.f.j	4
		931.2.f.k	4
		931.2.f.l	6
		931.2.f.m	6
		931.2.f.n	8
		931.2.f.o	8
		931.2.f.p	14
		931.2.f.q	20
		931.2.f.r	20
931.2.g	\(\chi_{931}(30, \cdot)\)	931.2.g.a	4	2
		931.2.g.b	4
		931.2.g.c	6
		931.2.g.d	6
		931.2.g.e	10
		931.2.g.f	10
		931.2.g.g	20
		931.2.g.h	24
		931.2.g.i	40
931.2.h	\(\chi_{931}(410, \cdot)\)	931.2.h.a	4	2
		931.2.h.b	4
		931.2.h.c	6
		931.2.h.d	6
		931.2.h.e	10
		931.2.h.f	10
		931.2.h.g	20
		931.2.h.h	24
		931.2.h.i	40
931.2.i	\(\chi_{931}(411, \cdot)\)	931.2.i.a	2	2
		931.2.i.b	2
		931.2.i.c	4
		931.2.i.d	4
		931.2.i.e	4
		931.2.i.f	12
		931.2.i.g	16
		931.2.i.h	80
931.2.o	\(\chi_{931}(227, \cdot)\)	931.2.o.a	4	2
		931.2.o.b	4
		931.2.o.c	4
		931.2.o.d	4
		931.2.o.e	6
		931.2.o.f	6
		931.2.o.g	8
		931.2.o.h	8
		931.2.o.i	80
931.2.p	\(\chi_{931}(293, \cdot)\)	931.2.p.a	2	2
		931.2.p.b	2
		931.2.p.c	2
		931.2.p.d	2
		931.2.p.e	4
		931.2.p.f	4
		931.2.p.g	16
		931.2.p.h	16
		931.2.p.i	80
931.2.s	\(\chi_{931}(31, \cdot)\)	931.2.s.a	2	2
		931.2.s.b	2
		931.2.s.c	4
		931.2.s.d	4
		931.2.s.e	4
		931.2.s.f	12
		931.2.s.g	16
		931.2.s.h	80
931.2.u	\(\chi_{931}(134, \cdot)\)	931.2.u.a	240	6
		931.2.u.b	264
931.2.v	\(\chi_{931}(177, \cdot)\)	931.2.v.a	6	6
		931.2.v.b	6
		931.2.v.c	30
		931.2.v.d	30
		931.2.v.e	30
		931.2.v.f	30
		931.2.v.g	60
		931.2.v.h	66
		931.2.v.i	120
931.2.w	\(\chi_{931}(99, \cdot)\)	931.2.w.a	6	6
		931.2.w.b	30
		931.2.w.c	30
		931.2.w.d	60
		931.2.w.e	66
		931.2.w.f	66
		931.2.w.g	120
931.2.x	\(\chi_{931}(226, \cdot)\)	931.2.x.a	6	6
		931.2.x.b	6
		931.2.x.c	30
		931.2.x.d	30
		931.2.x.e	30
		931.2.x.f	30
		931.2.x.g	60
		931.2.x.h	66
		931.2.x.i	120
931.2.z	\(\chi_{931}(132, \cdot)\)	931.2.z.a	12	6
		931.2.z.b	528
931.2.be	\(\chi_{931}(48, \cdot)\)	931.2.be.a	66	6
		931.2.be.b	66
		931.2.be.c	240
931.2.bf	\(\chi_{931}(325, \cdot)\)	931.2.bf.a	66	6
		931.2.bf.b	72
		931.2.bf.c	240
931.2.bj	\(\chi_{931}(117, \cdot)\)	931.2.bj.a	66	6
		931.2.bj.b	72
		931.2.bj.c	240
931.2.bk	\(\chi_{931}(11, \cdot)\)	931.2.bk.a	1104	12
931.2.bl	\(\chi_{931}(102, \cdot)\)	931.2.bl.a	1104	12
931.2.bm	\(\chi_{931}(39, \cdot)\)	931.2.bm.a	480	12
		931.2.bm.b	528
931.2.bn	\(\chi_{931}(64, \cdot)\)	931.2.bn.a	1080	12
931.2.bp	\(\chi_{931}(103, \cdot)\)	931.2.bp.a	1104	12
931.2.bs	\(\chi_{931}(27, \cdot)\)	931.2.bs.a	1080	12
931.2.bt	\(\chi_{931}(75, \cdot)\)	931.2.bt.a	24	12
		931.2.bt.b	1080
931.2.bz	\(\chi_{931}(12, \cdot)\)	931.2.bz.a	1104	12
931.2.ca	\(\chi_{931}(4, \cdot)\)	931.2.ca.a	3276	36
931.2.cb	\(\chi_{931}(9, \cdot)\)	931.2.cb.a	3276	36
931.2.cc	\(\chi_{931}(36, \cdot)\)	931.2.cc.a	3312	36
931.2.cd	\(\chi_{931}(10, \cdot)\)	931.2.cd.a	3276	36
931.2.ch	\(\chi_{931}(13, \cdot)\)	931.2.ch.a	3312	36
931.2.ci	\(\chi_{931}(3, \cdot)\)	931.2.ci.a	3276	36

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(931))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(931)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 2}\)