Space of modular forms of level 975 and weight 2

• Label: 975.2
• Level: 975
• Weight: 2
• Dimension: 22496
• Nonzero newspaces: 40
• Newform subspaces: 243
• Sturm bound: 134400
• Trace bound: 6

Defining parameters

Level:	$N$	=	$975 = 3 \cdot 5^{2} \cdot 13$
Weight:	$k$	=	$2$
Nonzero newspaces:			$40$
Newform subspaces:			$243$
Sturm bound:			$134400$
Trace bound:			$6$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(975))$.

	Total	New	Old
Modular forms	34944	23400	11544
Cusp forms	32257	22496	9761
Eisenstein series	2687	904	1783

Trace form

22496 * q + 2 * q^2 - 60 * q^3 - 106 * q^4 + 12 * q^5 - 80 * q^6 - 96 * q^7 + 60 * q^8 - 50 * q^9 - 124 * q^10 + 20 * q^11 - 14 * q^12 - 102 * q^13 + 72 * q^14 - 68 * q^15 - 146 * q^16 + 22 * q^17 - 52 * q^18 - 100 * q^19 - 72 * q^20 - 88 * q^21 - 128 * q^22 - 8 * q^23 - 144 * q^24 - 220 * q^25 + 66 * q^26 - 102 * q^27 - 160 * q^28 + 2 * q^29 - 124 * q^30 - 172 * q^31 + 26 * q^32 - 52 * q^33 - 68 * q^34 + 40 * q^35 - 174 * q^36 - 94 * q^37 - 16 * q^38 - 106 * q^39 - 388 * q^40 + 86 * q^41 - 192 * q^42 - 108 * q^43 - 36 * q^44 - 224 * q^45 - 156 * q^46 + 16 * q^47 - 368 * q^48 - 162 * q^49 - 236 * q^50 - 324 * q^51 - 440 * q^52 - 208 * q^53 - 548 * q^54 - 344 * q^55 - 396 * q^56 - 360 * q^57 - 490 * q^58 - 260 * q^59 - 412 * q^60 - 222 * q^61 - 452 * q^62 - 332 * q^63 - 596 * q^64 - 134 * q^65 - 508 * q^66 - 252 * q^67 - 386 * q^68 - 200 * q^69 - 200 * q^70 - 56 * q^71 - 318 * q^72 - 176 * q^73 - 86 * q^74 + 12 * q^75 - 708 * q^76 - 24 * q^77 - 302 * q^78 - 232 * q^79 + 140 * q^80 - 134 * q^81 - 10 * q^82 + 92 * q^83 - 104 * q^84 - 268 * q^85 + 104 * q^86 - 26 * q^87 - 80 * q^88 - 24 * q^89 - 48 * q^90 - 116 * q^91 + 104 * q^92 - 152 * q^93 - 284 * q^94 - 112 * q^95 - 78 * q^96 - 340 * q^97 - 34 * q^98 + 8 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(975))$

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
975.2.a	$\chi_{975}(1, \cdot)$	975.2.a.a	1	1
		975.2.a.b	1
		975.2.a.c	1
		975.2.a.d	1
		975.2.a.e	1
		975.2.a.f	1
		975.2.a.g	1
		975.2.a.h	1
		975.2.a.i	1
		975.2.a.j	1
		975.2.a.k	1
		975.2.a.l	2
		975.2.a.m	3
		975.2.a.n	3
		975.2.a.o	3
		975.2.a.p	3
		975.2.a.q	3
		975.2.a.r	5
		975.2.a.s	5
975.2.b	$\chi_{975}(376, \cdot)$	975.2.b.a	2	1
		975.2.b.b	2
		975.2.b.c	2
		975.2.b.d	2
		975.2.b.e	2
		975.2.b.f	4
		975.2.b.g	4
		975.2.b.h	4
		975.2.b.i	6
		975.2.b.j	6
		975.2.b.k	6
		975.2.b.l	6
975.2.c	$\chi_{975}(274, \cdot)$	975.2.c.a	2	1
		975.2.c.b	2
		975.2.c.c	2
		975.2.c.d	2
		975.2.c.e	2
		975.2.c.f	2
		975.2.c.g	2
		975.2.c.h	4
		975.2.c.i	6
		975.2.c.j	6
		975.2.c.k	6
975.2.h	$\chi_{975}(649, \cdot)$	975.2.h.a	2	1
		975.2.h.b	2
		975.2.h.c	2
		975.2.h.d	2
		975.2.h.e	4
		975.2.h.f	4
		975.2.h.g	4
		975.2.h.h	8
		975.2.h.i	12
975.2.i	$\chi_{975}(451, \cdot)$	975.2.i.a	2	2
		975.2.i.b	2
		975.2.i.c	2
		975.2.i.d	2
		975.2.i.e	2
		975.2.i.f	2
		975.2.i.g	2
		975.2.i.h	2
		975.2.i.i	2
		975.2.i.j	4
		975.2.i.k	4
		975.2.i.l	6
		975.2.i.m	6
		975.2.i.n	12
		975.2.i.o	12
		975.2.i.p	12
		975.2.i.q	12
975.2.k	$\chi_{975}(307, \cdot)$	975.2.k.a	4	2
		975.2.k.b	4
		975.2.k.c	8
		975.2.k.d	28
		975.2.k.e	40
975.2.m	$\chi_{975}(443, \cdot)$	975.2.m.a	32	2
		975.2.m.b	32
		975.2.m.c	32
		975.2.m.d	48
975.2.n	$\chi_{975}(749, \cdot)$	975.2.n.a	4	2
		975.2.n.b	4
		975.2.n.c	4
		975.2.n.d	4
		975.2.n.e	4
		975.2.n.f	4
		975.2.n.g	4
		975.2.n.h	4
		975.2.n.i	4
		975.2.n.j	4
		975.2.n.k	4
		975.2.n.l	4
		975.2.n.m	8
		975.2.n.n	8
		975.2.n.o	8
		975.2.n.p	8
		975.2.n.q	40
		975.2.n.r	40
975.2.o	$\chi_{975}(476, \cdot)$	975.2.o.a	4	2
		975.2.o.b	4
		975.2.o.c	4
		975.2.o.d	4
		975.2.o.e	4
		975.2.o.f	4
		975.2.o.g	4
		975.2.o.h	4
		975.2.o.i	4
		975.2.o.j	4
		975.2.o.k	4
		975.2.o.l	8
		975.2.o.m	8
		975.2.o.n	8
		975.2.o.o	8
		975.2.o.p	40
		975.2.o.q	48
975.2.s	$\chi_{975}(818, \cdot)$	975.2.s.a	8	2
		975.2.s.b	8
		975.2.s.c	16
		975.2.s.d	32
		975.2.s.e	32
		975.2.s.f	64
975.2.t	$\chi_{975}(268, \cdot)$	975.2.t.a	4	2
		975.2.t.b	4
		975.2.t.c	8
		975.2.t.d	28
		975.2.t.e	40
975.2.v	$\chi_{975}(196, \cdot)$	975.2.v.a	52	4
		975.2.v.b	52
		975.2.v.c	68
		975.2.v.d	68
975.2.w	$\chi_{975}(49, \cdot)$	975.2.w.a	4	2
		975.2.w.b	4
		975.2.w.c	4
		975.2.w.d	4
		975.2.w.e	4
		975.2.w.f	4
		975.2.w.g	8
		975.2.w.h	8
		975.2.w.i	8
		975.2.w.j	8
		975.2.w.k	24
975.2.bb	$\chi_{975}(724, \cdot)$	975.2.bb.a	4	2
		975.2.bb.b	4
		975.2.bb.c	4
		975.2.bb.d	4
		975.2.bb.e	4
		975.2.bb.f	4
		975.2.bb.g	4
		975.2.bb.h	4
		975.2.bb.i	8
		975.2.bb.j	12
		975.2.bb.k	12
		975.2.bb.l	24
975.2.bc	$\chi_{975}(751, \cdot)$	975.2.bc.a	2	2
		975.2.bc.b	2
		975.2.bc.c	2
		975.2.bc.d	2
		975.2.bc.e	2
		975.2.bc.f	2
		975.2.bc.g	2
		975.2.bc.h	4
		975.2.bc.i	8
		975.2.bc.j	8
		975.2.bc.k	12
		975.2.bc.l	12
		975.2.bc.m	16
		975.2.bc.n	16
975.2.bf	$\chi_{975}(64, \cdot)$	975.2.bf.a	288	4
975.2.bg	$\chi_{975}(79, \cdot)$	975.2.bg.a	104	4
		975.2.bg.b	136
975.2.bh	$\chi_{975}(181, \cdot)$	975.2.bh.a	8	4
		975.2.bh.b	128
		975.2.bh.c	136
975.2.bl	$\chi_{975}(193, \cdot)$	975.2.bl.a	8	4
		975.2.bl.b	8
		975.2.bl.c	8
		975.2.bl.d	8
		975.2.bl.e	16
		975.2.bl.f	16
		975.2.bl.g	16
		975.2.bl.h	32
		975.2.bl.i	56
975.2.bn	$\chi_{975}(218, \cdot)$	975.2.bn.a	8	4
		975.2.bn.b	8
		975.2.bn.c	64
		975.2.bn.d	96
		975.2.bn.e	144
975.2.bo	$\chi_{975}(176, \cdot)$	975.2.bo.a	4	4
		975.2.bo.b	4
		975.2.bo.c	4
		975.2.bo.d	8
		975.2.bo.e	72
		975.2.bo.f	72
		975.2.bo.g	72
		975.2.bo.h	96
975.2.bp	$\chi_{975}(149, \cdot)$	975.2.bp.a	4	4
		975.2.bp.b	4
		975.2.bp.c	4
		975.2.bp.d	4
		975.2.bp.e	8
		975.2.bp.f	8
		975.2.bp.g	72
		975.2.bp.h	72
		975.2.bp.i	72
		975.2.bp.j	72
975.2.bt	$\chi_{975}(68, \cdot)$	975.2.bt.a	8	4
		975.2.bt.b	8
		975.2.bt.c	8
		975.2.bt.d	8
		975.2.bt.e	8
		975.2.bt.f	8
		975.2.bt.g	8
		975.2.bt.h	8
		975.2.bt.i	8
		975.2.bt.j	8
		975.2.bt.k	48
		975.2.bt.l	96
		975.2.bt.m	96
975.2.bu	$\chi_{975}(7, \cdot)$	975.2.bu.a	8	4
		975.2.bu.b	8
		975.2.bu.c	8
		975.2.bu.d	8
		975.2.bu.e	16
		975.2.bu.f	16
		975.2.bu.g	16
		975.2.bu.h	32
		975.2.bu.i	56
975.2.bw	$\chi_{975}(16, \cdot)$	975.2.bw.a	288	8
		975.2.bw.b	288
975.2.bx	$\chi_{975}(73, \cdot)$	975.2.bx.a	560	8
975.2.bz	$\chi_{975}(38, \cdot)$	975.2.bz.a	64	8
		975.2.bz.b	1024
975.2.cd	$\chi_{975}(86, \cdot)$	975.2.cd.a	1088	8
975.2.ce	$\chi_{975}(44, \cdot)$	975.2.ce.a	1088	8
975.2.cf	$\chi_{975}(53, \cdot)$	975.2.cf.a	960	8
975.2.ci	$\chi_{975}(112, \cdot)$	975.2.ci.a	560	8
975.2.cl	$\chi_{975}(121, \cdot)$	975.2.cl.a	272	8
		975.2.cl.b	272
975.2.cm	$\chi_{975}(94, \cdot)$	975.2.cm.a	544	8
975.2.cn	$\chi_{975}(4, \cdot)$	975.2.cn.a	576	8
975.2.cq	$\chi_{975}(28, \cdot)$	975.2.cq.a	1120	16
975.2.cs	$\chi_{975}(113, \cdot)$	975.2.cs.a	2176	16
975.2.cw	$\chi_{975}(59, \cdot)$	975.2.cw.a	2176	16
975.2.cx	$\chi_{975}(11, \cdot)$	975.2.cx.a	2176	16
975.2.cy	$\chi_{975}(17, \cdot)$	975.2.cy.a	2176	16
975.2.db	$\chi_{975}(67, \cdot)$	975.2.db.a	1120	16

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(975))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(975)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(325))$$^{\oplus 2}$