Space of modular forms of level 725 and weight 2

• Label: 725.2
• Level: 725
• Weight: 2
• Dimension: 18757
• Nonzero newspaces: 24
• Newform subspaces: 83
• Sturm bound: 84000
• Trace bound: 4

Defining parameters

Level:	$N$	=	$725 = 5^{2} \cdot 29$
Weight:	$k$	=	$2$
Nonzero newspaces:			$24$
Newform subspaces:			$83$
Sturm bound:			$84000$
Trace bound:			$4$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(725))$.

	Total	New	Old
Modular forms	21784	19863	1921
Cusp forms	20217	18757	1460
Eisenstein series	1567	1106	461

Trace form

18757 * q - 168 * q^2 - 170 * q^3 - 176 * q^4 - 214 * q^5 - 282 * q^6 - 178 * q^7 - 192 * q^8 - 188 * q^9 - 234 * q^10 - 282 * q^11 - 218 * q^12 - 190 * q^13 - 210 * q^14 - 244 * q^15 - 288 * q^16 - 178 * q^17 - 190 * q^18 - 162 * q^19 - 204 * q^20 - 310 * q^21 - 182 * q^22 - 184 * q^23 - 226 * q^24 - 194 * q^25 - 597 * q^26 - 224 * q^27 - 224 * q^28 - 210 * q^29 - 468 * q^30 - 310 * q^31 - 274 * q^32 - 260 * q^33 - 255 * q^34 - 264 * q^35 - 412 * q^36 - 242 * q^37 - 250 * q^38 - 222 * q^39 - 254 * q^40 - 302 * q^41 - 154 * q^42 - 170 * q^43 - 204 * q^44 - 174 * q^45 - 352 * q^46 - 206 * q^47 - 222 * q^48 - 222 * q^49 - 174 * q^50 - 598 * q^51 - 250 * q^52 - 243 * q^53 - 268 * q^54 - 244 * q^55 - 440 * q^56 - 232 * q^57 - 360 * q^58 - 392 * q^59 - 204 * q^60 - 358 * q^61 - 232 * q^62 - 302 * q^63 - 322 * q^64 - 234 * q^65 - 442 * q^66 - 274 * q^67 - 272 * q^68 - 270 * q^69 - 284 * q^70 - 392 * q^71 - 366 * q^72 - 293 * q^73 - 268 * q^74 - 244 * q^75 - 686 * q^76 - 264 * q^77 - 350 * q^78 - 270 * q^79 - 234 * q^80 - 460 * q^81 - 230 * q^82 - 166 * q^83 - 420 * q^84 - 154 * q^85 - 436 * q^86 - 232 * q^87 - 472 * q^88 - 162 * q^89 - 174 * q^90 - 366 * q^91 - 386 * q^92 - 214 * q^93 - 186 * q^94 - 244 * q^95 - 560 * q^96 - 155 * q^97 - 366 * q^98 - 396 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(725))$

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
725.2.a	$\chi_{725}(1, \cdot)$	725.2.a.a	1	1
		725.2.a.b	2
		725.2.a.c	2
		725.2.a.d	3
		725.2.a.e	3
		725.2.a.f	4
		725.2.a.g	4
		725.2.a.h	5
		725.2.a.i	5
		725.2.a.j	5
		725.2.a.k	5
		725.2.a.l	6
725.2.b	$\chi_{725}(349, \cdot)$	725.2.b.a	2	1
		725.2.b.b	4
		725.2.b.c	4
		725.2.b.d	6
		725.2.b.e	6
		725.2.b.f	10
		725.2.b.g	10
725.2.c	$\chi_{725}(376, \cdot)$	725.2.c.a	2	1
		725.2.c.b	2
		725.2.c.c	2
		725.2.c.d	4
		725.2.c.e	6
		725.2.c.f	8
		725.2.c.g	10
		725.2.c.h	10
725.2.d	$\chi_{725}(724, \cdot)$	725.2.d.a	4	1
		725.2.d.b	8
		725.2.d.c	12
		725.2.d.d	20
725.2.e	$\chi_{725}(157, \cdot)$	725.2.e.a	4	2
		725.2.e.b	16
		725.2.e.c	26
		725.2.e.d	40
725.2.j	$\chi_{725}(307, \cdot)$	725.2.j.a	4	2
		725.2.j.b	16
		725.2.j.c	26
		725.2.j.d	40
725.2.k	$\chi_{725}(146, \cdot)$	725.2.k.a	4	4
		725.2.k.b	128
		725.2.k.c	148
725.2.l	$\chi_{725}(226, \cdot)$	725.2.l.a	6	6
		725.2.l.b	6
		725.2.l.c	6
		725.2.l.d	24
		725.2.l.e	36
		725.2.l.f	54
		725.2.l.g	54
		725.2.l.h	84
725.2.m	$\chi_{725}(144, \cdot)$	725.2.m.a	288	4
725.2.n	$\chi_{725}(59, \cdot)$	725.2.n.a	128	4
		725.2.n.b	152
725.2.o	$\chi_{725}(86, \cdot)$	725.2.o.a	296	4
725.2.p	$\chi_{725}(149, \cdot)$	725.2.p.a	24	6
		725.2.p.b	48
		725.2.p.c	72
		725.2.p.d	120
725.2.q	$\chi_{725}(51, \cdot)$	725.2.q.a	12	6
		725.2.q.b	24
		725.2.q.c	36
		725.2.q.d	60
		725.2.q.e	60
		725.2.q.f	72
725.2.r	$\chi_{725}(24, \cdot)$	725.2.r.a	12	6
		725.2.r.b	12
		725.2.r.c	48
		725.2.r.d	72
		725.2.r.e	108
725.2.s	$\chi_{725}(17, \cdot)$	725.2.s.a	584	8
725.2.x	$\chi_{725}(12, \cdot)$	725.2.x.a	584	8
725.2.y	$\chi_{725}(18, \cdot)$	725.2.y.a	120	12
		725.2.y.b	156
		725.2.y.c	240
725.2.bd	$\chi_{725}(43, \cdot)$	725.2.bd.a	120	12
		725.2.bd.b	156
		725.2.bd.c	240
725.2.be	$\chi_{725}(16, \cdot)$	725.2.be.a	1728	24
725.2.bf	$\chi_{725}(6, \cdot)$	725.2.bf.a	1776	24
725.2.bg	$\chi_{725}(54, \cdot)$	725.2.bg.a	1776	24
725.2.bh	$\chi_{725}(4, \cdot)$	725.2.bh.a	1728	24
725.2.bi	$\chi_{725}(3, \cdot)$	725.2.bi.a	3504	48
725.2.bn	$\chi_{725}(2, \cdot)$	725.2.bn.a	3504	48

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(725))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(725)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$^{\oplus 2}$