Space of modular forms of level 3825 and weight 2

• Label: 3825.2
• Level: 3825
• Weight: 2
• Dimension: 372858
• Nonzero newspaces: 72
• Sturm bound: 2073600
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 3825 = 3^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 72 \)
Sturm bound:			\(2073600\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3825))\).

	Total	New	Old
Modular forms	525568	378392	147176
Cusp forms	511233	372858	138375
Eisenstein series	14335	5534	8801

Trace form

372858 * q - 280 * q^2 - 368 * q^3 - 296 * q^4 - 342 * q^5 - 592 * q^6 - 300 * q^7 - 264 * q^8 - 352 * q^9 - 1002 * q^10 - 420 * q^11 - 304 * q^12 - 268 * q^13 - 220 * q^14 - 424 * q^15 - 428 * q^16 - 276 * q^17 - 688 * q^18 - 804 * q^19 - 204 * q^20 - 528 * q^21 - 156 * q^22 - 172 * q^23 - 192 * q^24 - 258 * q^25 - 756 * q^26 - 272 * q^27 - 652 * q^28 - 144 * q^29 - 368 * q^30 - 420 * q^31 - 122 * q^32 - 304 * q^33 - 293 * q^34 - 704 * q^35 - 656 * q^36 - 770 * q^37 - 272 * q^38 - 432 * q^39 - 270 * q^40 - 504 * q^41 - 384 * q^42 - 276 * q^43 - 224 * q^44 - 488 * q^45 - 1148 * q^46 - 212 * q^47 - 416 * q^48 - 34 * q^49 - 206 * q^50 - 1168 * q^51 - 144 * q^52 - 70 * q^53 - 240 * q^54 - 868 * q^55 - 172 * q^56 - 192 * q^57 + 32 * q^58 + 8 * q^59 - 552 * q^60 - 372 * q^61 - 88 * q^62 - 248 * q^63 - 708 * q^64 - 490 * q^65 - 368 * q^66 - 436 * q^67 - 506 * q^68 - 792 * q^69 - 556 * q^70 - 300 * q^71 - 736 * q^72 - 784 * q^73 - 716 * q^74 - 768 * q^75 - 696 * q^76 - 604 * q^77 - 896 * q^78 - 348 * q^79 - 914 * q^80 - 848 * q^81 - 840 * q^82 - 720 * q^83 - 1024 * q^84 - 213 * q^85 - 1076 * q^86 - 616 * q^87 + 372 * q^88 - 354 * q^89 - 880 * q^90 - 812 * q^91 + 220 * q^92 - 488 * q^93 + 788 * q^94 - 116 * q^95 - 640 * q^96 + 356 * q^97 + 236 * q^98 - 272 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3825))\)

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
3825.2.a	\(\chi_{3825}(1, \cdot)\)	3825.2.a.a	1	1
		3825.2.a.b	1
		3825.2.a.c	1
		3825.2.a.d	1
		3825.2.a.e	1
		3825.2.a.f	1
		3825.2.a.g	1
		3825.2.a.h	1
		3825.2.a.i	1
		3825.2.a.j	1
		3825.2.a.k	1
		3825.2.a.l	1
		3825.2.a.m	1
		3825.2.a.n	1
		3825.2.a.o	1
		3825.2.a.p	2
		3825.2.a.q	2
		3825.2.a.r	2
		3825.2.a.s	2
		3825.2.a.t	2
		3825.2.a.u	2
		3825.2.a.v	2
		3825.2.a.w	2
		3825.2.a.x	2
		3825.2.a.y	2
		3825.2.a.z	2
		3825.2.a.ba	3
		3825.2.a.bb	3
		3825.2.a.bc	3
		3825.2.a.bd	3
		3825.2.a.be	3
		3825.2.a.bf	3
		3825.2.a.bg	3
		3825.2.a.bh	4
		3825.2.a.bi	4
		3825.2.a.bj	4
		3825.2.a.bk	5
		3825.2.a.bl	5
		3825.2.a.bm	5
		3825.2.a.bn	5
		3825.2.a.bo	5
		3825.2.a.bp	5
		3825.2.a.bq	5
		3825.2.a.br	5
		3825.2.a.bs	8
		3825.2.a.bt	8
3825.2.b	\(\chi_{3825}(2449, \cdot)\)	n/a	120	1
3825.2.d	\(\chi_{3825}(424, \cdot)\)	n/a	132	1
3825.2.g	\(\chi_{3825}(1801, \cdot)\)	n/a	140	1
3825.2.i	\(\chi_{3825}(1276, \cdot)\)	n/a	608	2
3825.2.k	\(\chi_{3825}(676, \cdot)\)	n/a	280	2
3825.2.l	\(\chi_{3825}(1007, \cdot)\)	n/a	216	2
3825.2.n	\(\chi_{3825}(1718, \cdot)\)	n/a	192	2
3825.2.p	\(\chi_{3825}(1682, \cdot)\)	n/a	216	2
3825.2.s	\(\chi_{3825}(557, \cdot)\)	n/a	216	2
3825.2.t	\(\chi_{3825}(3124, \cdot)\)	n/a	264	2
3825.2.v	\(\chi_{3825}(766, \cdot)\)	n/a	800	4
3825.2.x	\(\chi_{3825}(526, \cdot)\)	n/a	672	2
3825.2.ba	\(\chi_{3825}(1699, \cdot)\)	n/a	640	2
3825.2.bc	\(\chi_{3825}(1174, \cdot)\)	n/a	576	2
3825.2.be	\(\chi_{3825}(332, \cdot)\)	n/a	432	4
3825.2.bf	\(\chi_{3825}(451, \cdot)\)	n/a	556	4
3825.2.bi	\(\chi_{3825}(1324, \cdot)\)	n/a	536	4
3825.2.bj	\(\chi_{3825}(2168, \cdot)\)	n/a	432	4
3825.2.bl	\(\chi_{3825}(271, \cdot)\)	n/a	888	4
3825.2.bp	\(\chi_{3825}(154, \cdot)\)	n/a	800	4
3825.2.br	\(\chi_{3825}(1189, \cdot)\)	n/a	896	4
3825.2.bt	\(\chi_{3825}(574, \cdot)\)	n/a	1280	4
3825.2.bu	\(\chi_{3825}(293, \cdot)\)	n/a	1280	4
3825.2.bw	\(\chi_{3825}(407, \cdot)\)	n/a	1280	4
3825.2.by	\(\chi_{3825}(443, \cdot)\)	n/a	1152	4
3825.2.cb	\(\chi_{3825}(1118, \cdot)\)	n/a	1280	4
3825.2.cc	\(\chi_{3825}(1951, \cdot)\)	n/a	1344	4
3825.2.ce	\(\chi_{3825}(256, \cdot)\)	n/a	3840	8
3825.2.cg	\(\chi_{3825}(343, \cdot)\)	n/a	1064	8
3825.2.ch	\(\chi_{3825}(224, \cdot)\)	n/a	864	8
3825.2.cj	\(\chi_{3825}(1151, \cdot)\)	n/a	912	8
3825.2.cl	\(\chi_{3825}(82, \cdot)\)	n/a	1064	8
3825.2.co	\(\chi_{3825}(64, \cdot)\)	n/a	1792	8
3825.2.cq	\(\chi_{3825}(98, \cdot)\)	n/a	1440	8
3825.2.cr	\(\chi_{3825}(152, \cdot)\)	n/a	1440	8
3825.2.ct	\(\chi_{3825}(188, \cdot)\)	n/a	1280	8
3825.2.cv	\(\chi_{3825}(548, \cdot)\)	n/a	1440	8
3825.2.cx	\(\chi_{3825}(361, \cdot)\)	n/a	1776	8
3825.2.da	\(\chi_{3825}(32, \cdot)\)	n/a	2560	8
3825.2.db	\(\chi_{3825}(49, \cdot)\)	n/a	2560	8
3825.2.de	\(\chi_{3825}(76, \cdot)\)	n/a	2688	8
3825.2.df	\(\chi_{3825}(1607, \cdot)\)	n/a	2560	8
3825.2.dh	\(\chi_{3825}(169, \cdot)\)	n/a	4288	8
3825.2.dj	\(\chi_{3825}(409, \cdot)\)	n/a	3840	8
3825.2.dn	\(\chi_{3825}(16, \cdot)\)	n/a	4288	8
3825.2.do	\(\chi_{3825}(8, \cdot)\)	n/a	2880	16
3825.2.dq	\(\chi_{3825}(19, \cdot)\)	n/a	3552	16
3825.2.dt	\(\chi_{3825}(406, \cdot)\)	n/a	3584	16
3825.2.dv	\(\chi_{3825}(53, \cdot)\)	n/a	2880	16
3825.2.dx	\(\chi_{3825}(193, \cdot)\)	n/a	5120	16
3825.2.dz	\(\chi_{3825}(176, \cdot)\)	n/a	5376	16
3825.2.eb	\(\chi_{3825}(74, \cdot)\)	n/a	5120	16
3825.2.ec	\(\chi_{3825}(7, \cdot)\)	n/a	5120	16
3825.2.ef	\(\chi_{3825}(106, \cdot)\)	n/a	8576	16
3825.2.eh	\(\chi_{3825}(38, \cdot)\)	n/a	8576	16
3825.2.ei	\(\chi_{3825}(137, \cdot)\)	n/a	7680	16
3825.2.ek	\(\chi_{3825}(203, \cdot)\)	n/a	8576	16
3825.2.em	\(\chi_{3825}(353, \cdot)\)	n/a	8576	16
3825.2.eo	\(\chi_{3825}(4, \cdot)\)	n/a	8576	16
3825.2.er	\(\chi_{3825}(28, \cdot)\)	n/a	7136	32
3825.2.et	\(\chi_{3825}(71, \cdot)\)	n/a	5760	32
3825.2.ev	\(\chi_{3825}(44, \cdot)\)	n/a	5760	32
3825.2.ew	\(\chi_{3825}(73, \cdot)\)	n/a	7136	32
3825.2.ey	\(\chi_{3825}(77, \cdot)\)	n/a	17152	32
3825.2.fa	\(\chi_{3825}(121, \cdot)\)	n/a	17152	32
3825.2.fd	\(\chi_{3825}(94, \cdot)\)	n/a	17152	32
3825.2.ff	\(\chi_{3825}(2, \cdot)\)	n/a	17152	32
3825.2.fh	\(\chi_{3825}(88, \cdot)\)	n/a	34304	64
3825.2.fi	\(\chi_{3825}(14, \cdot)\)	n/a	34304	64
3825.2.fk	\(\chi_{3825}(11, \cdot)\)	n/a	34304	64
3825.2.fm	\(\chi_{3825}(22, \cdot)\)	n/a	34304	64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3825))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3825)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(765))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1275))\)\(^{\oplus 2}\)