Space of modular forms of level 325 and weight 10

• Label: 325.10
• Level: 325
• Weight: 10
• Dimension: 34199
• Nonzero newspaces: 24
• Sturm bound: 84000
• Trace bound: 3

Defining parameters

Level:	$N$	=	$325 = 5^{2} \cdot 13$
Weight:	$k$	=	$10$
Nonzero newspaces:			$24$
Sturm bound:			$84000$
Trace bound:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{10}(\Gamma_1(325))$.

	Total	New	Old
Modular forms	38136	34649	3487
Cusp forms	37464	34199	3265
Eisenstein series	672	450	222

Trace form

34199 * q - 130 * q^2 + 526 * q^3 - 3146 * q^4 + 3454 * q^5 - 6554 * q^6 + 21658 * q^7 - 87322 * q^8 + 29730 * q^9 - 140896 * q^10 + 332466 * q^11 + 493824 * q^12 - 110328 * q^13 - 3231592 * q^14 - 326016 * q^15 + 8045670 * q^16 - 795989 * q^17 + 2211232 * q^18 - 4216726 * q^19 - 11172916 * q^20 + 9440406 * q^21 + 16778668 * q^22 + 1389810 * q^23 + 5357098 * q^24 + 14282434 * q^25 - 2154180 * q^26 - 24539252 * q^27 - 47464832 * q^28 + 888159 * q^29 + 37043764 * q^30 - 24134690 * q^31 + 4693992 * q^32 - 32795490 * q^33 + 95220974 * q^34 + 3615824 * q^35 - 46825590 * q^36 - 84127875 * q^37 - 303515500 * q^38 - 83776236 * q^39 + 294930728 * q^40 + 67542649 * q^41 + 43975024 * q^42 - 24043414 * q^43 - 415863236 * q^44 - 505527106 * q^45 - 112967270 * q^46 + 184137874 * q^47 + 904245594 * q^48 + 259479108 * q^49 + 1100057276 * q^50 - 719325180 * q^51 - 2071464288 * q^52 - 536409226 * q^53 + 582232592 * q^54 + 134681556 * q^55 + 2388993304 * q^56 + 485883530 * q^57 - 1089675478 * q^58 - 1761757542 * q^59 - 2474531908 * q^60 - 1346666543 * q^61 + 209994402 * q^62 + 4603239530 * q^63 + 9477808356 * q^64 + 3054186265 * q^65 + 3658300412 * q^66 - 2967583250 * q^67 - 11487389440 * q^68 - 11125759478 * q^69 - 7420983292 * q^70 - 1541920498 * q^71 + 582871332 * q^72 + 5557806318 * q^73 + 18840475182 * q^74 + 10728929704 * q^75 + 8553332790 * q^76 - 3612071808 * q^77 - 13841338508 * q^78 - 12518608488 * q^79 - 17418506092 * q^80 - 1267209192 * q^81 + 4989752946 * q^82 + 2279285022 * q^83 + 14211632792 * q^84 + 8071653134 * q^85 + 8440530780 * q^86 + 18724634690 * q^87 + 11260745024 * q^88 - 9189029028 * q^89 - 23154467196 * q^90 - 12574388992 * q^91 - 21134622144 * q^92 - 7109684366 * q^93 - 399939766 * q^94 - 497210516 * q^95 + 20600714096 * q^96 + 22371681842 * q^97 + 29443839538 * q^98 + 20930729670 * q^99

Decomposition of $S_{10}^{\mathrm{new}}(\Gamma_1(325))$

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
325.10.a	$\chi_{325}(1, \cdot)$	325.10.a.a	4	1
		325.10.a.b	5
		325.10.a.c	7
		325.10.a.d	9
		325.10.a.e	10
		325.10.a.f	10
		325.10.a.g	17
		325.10.a.h	17
		325.10.a.i	19
		325.10.a.j	19
		325.10.a.k	27
		325.10.a.l	27
325.10.b	$\chi_{325}(274, \cdot)$	n/a	162	1
325.10.c	$\chi_{325}(51, \cdot)$	n/a	196	1
325.10.d	$\chi_{325}(324, \cdot)$	n/a	188	1
325.10.e	$\chi_{325}(126, \cdot)$	n/a	394	2
325.10.f	$\chi_{325}(18, \cdot)$	n/a	374	2
325.10.k	$\chi_{325}(57, \cdot)$	n/a	374	2
325.10.l	$\chi_{325}(66, \cdot)$	n/a	1080	4
325.10.m	$\chi_{325}(49, \cdot)$	n/a	376	2
325.10.n	$\chi_{325}(101, \cdot)$	n/a	392	2
325.10.o	$\chi_{325}(74, \cdot)$	n/a	372	2
325.10.p	$\chi_{325}(64, \cdot)$	n/a	1248	4
325.10.q	$\chi_{325}(116, \cdot)$	n/a	1256	4
325.10.r	$\chi_{325}(14, \cdot)$	n/a	1080	4
325.10.s	$\chi_{325}(32, \cdot)$	n/a	748	4
325.10.x	$\chi_{325}(7, \cdot)$	n/a	748	4
325.10.y	$\chi_{325}(16, \cdot)$	n/a	2496	8
325.10.z	$\chi_{325}(8, \cdot)$	n/a	2504	8
325.10.be	$\chi_{325}(47, \cdot)$	n/a	2504	8
325.10.bf	$\chi_{325}(9, \cdot)$	n/a	2512	8
325.10.bg	$\chi_{325}(36, \cdot)$	n/a	2512	8
325.10.bh	$\chi_{325}(4, \cdot)$	n/a	2496	8
325.10.bi	$\chi_{325}(28, \cdot)$	n/a	5008	16
325.10.bn	$\chi_{325}(2, \cdot)$	n/a	5008	16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of $S_{10}^{\mathrm{old}}(\Gamma_1(325))$ into lower level spaces

$S_{10}^{\mathrm{old}}(\Gamma_1(325)) \cong$ $S_{10}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 6}$$\oplus$$S_{10}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 4}$$\oplus$$S_{10}^{\mathrm{new}}(\Gamma_1(13))$$^{\oplus 3}$$\oplus$$S_{10}^{\mathrm{new}}(\Gamma_1(25))$$^{\oplus 2}$$\oplus$$S_{10}^{\mathrm{new}}(\Gamma_1(65))$$^{\oplus 2}$