Space of modular forms of level 2475 and weight 2

• Label: 2475.2
• Level: 2475
• Weight: 2
• Dimension: 153318
• Nonzero newspaces: 84
• Sturm bound: 864000
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 84 \)
Sturm bound:			\(864000\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2475))\).

	Total	New	Old
Modular forms	220480	156638	63842
Cusp forms	211521	153318	58203
Eisenstein series	8959	3320	5639

Trace form

153318 * q - 163 * q^2 - 212 * q^3 - 179 * q^4 - 198 * q^5 - 340 * q^6 - 188 * q^7 - 157 * q^8 - 196 * q^9 - 570 * q^10 - 274 * q^11 - 408 * q^12 - 148 * q^13 - 102 * q^14 - 232 * q^15 - 233 * q^16 - 122 * q^17 - 116 * q^18 - 460 * q^19 - 60 * q^20 - 276 * q^21 - 139 * q^22 - 237 * q^23 - 6 * q^24 - 114 * q^25 - 316 * q^26 - 86 * q^27 - 188 * q^28 + 28 * q^29 - 176 * q^30 - 179 * q^31 + 97 * q^32 - 154 * q^33 - 184 * q^34 - 176 * q^35 - 334 * q^36 - 377 * q^37 - 74 * q^38 - 278 * q^39 - 46 * q^40 - 352 * q^41 - 264 * q^42 - 108 * q^43 - 81 * q^44 - 616 * q^45 - 566 * q^46 - 130 * q^47 - 380 * q^48 + 132 * q^49 + 18 * q^50 - 650 * q^51 + 408 * q^52 + 108 * q^53 - 116 * q^54 - 498 * q^55 - 88 * q^56 - 36 * q^57 + 504 * q^58 + 271 * q^59 - 360 * q^60 + 12 * q^61 + 296 * q^62 - 60 * q^63 - 159 * q^64 - 286 * q^65 - 162 * q^66 - 259 * q^67 - 240 * q^68 - 140 * q^69 - 500 * q^70 - 101 * q^71 - 494 * q^72 - 638 * q^73 - 638 * q^74 - 576 * q^75 - 694 * q^76 - 354 * q^77 - 900 * q^78 - 428 * q^79 - 1090 * q^80 - 596 * q^81 - 890 * q^82 - 858 * q^83 - 1038 * q^84 - 282 * q^85 - 992 * q^86 - 656 * q^87 - 365 * q^88 - 859 * q^89 - 688 * q^90 - 688 * q^91 - 564 * q^92 - 560 * q^93 + 374 * q^94 - 20 * q^95 - 982 * q^96 + 333 * q^97 - 127 * q^98 - 420 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2475))\)

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
2475.2.a	\(\chi_{2475}(1, \cdot)\)	2475.2.a.a	1	1
		2475.2.a.b	1
		2475.2.a.c	1
		2475.2.a.d	1
		2475.2.a.e	1
		2475.2.a.f	1
		2475.2.a.g	1
		2475.2.a.h	1
		2475.2.a.i	1
		2475.2.a.j	1
		2475.2.a.k	1
		2475.2.a.l	2
		2475.2.a.m	2
		2475.2.a.n	2
		2475.2.a.o	2
		2475.2.a.p	2
		2475.2.a.q	2
		2475.2.a.r	2
		2475.2.a.s	2
		2475.2.a.t	2
		2475.2.a.u	2
		2475.2.a.v	2
		2475.2.a.w	2
		2475.2.a.x	2
		2475.2.a.y	3
		2475.2.a.z	3
		2475.2.a.ba	3
		2475.2.a.bb	3
		2475.2.a.bc	3
		2475.2.a.bd	3
		2475.2.a.be	3
		2475.2.a.bf	4
		2475.2.a.bg	4
		2475.2.a.bh	4
		2475.2.a.bi	4
		2475.2.a.bj	4
2475.2.c	\(\chi_{2475}(199, \cdot)\)	2475.2.c.a	2	1
		2475.2.c.b	2
		2475.2.c.c	2
		2475.2.c.d	2
		2475.2.c.e	2
		2475.2.c.f	2
		2475.2.c.g	2
		2475.2.c.h	2
		2475.2.c.i	4
		2475.2.c.j	4
		2475.2.c.k	4
		2475.2.c.l	4
		2475.2.c.m	4
		2475.2.c.n	4
		2475.2.c.o	4
		2475.2.c.p	4
		2475.2.c.q	6
		2475.2.c.r	6
		2475.2.c.s	8
		2475.2.c.t	8
2475.2.d	\(\chi_{2475}(2474, \cdot)\)	2475.2.d.a	8	1
		2475.2.d.b	16
		2475.2.d.c	16
		2475.2.d.d	32
2475.2.f	\(\chi_{2475}(2276, \cdot)\)	2475.2.f.a	2	1
		2475.2.f.b	2
		2475.2.f.c	2
		2475.2.f.d	2
		2475.2.f.e	4
		2475.2.f.f	16
		2475.2.f.g	16
		2475.2.f.h	16
		2475.2.f.i	16
2475.2.i	\(\chi_{2475}(826, \cdot)\)	n/a	380	2
2475.2.k	\(\chi_{2475}(307, \cdot)\)	n/a	176	2
2475.2.l	\(\chi_{2475}(782, \cdot)\)	n/a	120	2
2475.2.n	\(\chi_{2475}(361, \cdot)\)	n/a	592	4
2475.2.o	\(\chi_{2475}(676, \cdot)\)	n/a	368	4
2475.2.p	\(\chi_{2475}(631, \cdot)\)	n/a	592	4
2475.2.q	\(\chi_{2475}(181, \cdot)\)	n/a	592	4
2475.2.r	\(\chi_{2475}(496, \cdot)\)	n/a	504	4
2475.2.s	\(\chi_{2475}(91, \cdot)\)	n/a	592	4
2475.2.u	\(\chi_{2475}(626, \cdot)\)	n/a	444	2
2475.2.w	\(\chi_{2475}(824, \cdot)\)	n/a	424	2
2475.2.z	\(\chi_{2475}(1024, \cdot)\)	n/a	360	2
2475.2.ba	\(\chi_{2475}(1304, \cdot)\)	n/a	480	4
2475.2.bd	\(\chi_{2475}(379, \cdot)\)	n/a	592	4
2475.2.bf	\(\chi_{2475}(296, \cdot)\)	n/a	480	4
2475.2.bl	\(\chi_{2475}(1106, \cdot)\)	n/a	480	4
2475.2.bn	\(\chi_{2475}(611, \cdot)\)	n/a	480	4
2475.2.bq	\(\chi_{2475}(701, \cdot)\)	n/a	304	4
2475.2.br	\(\chi_{2475}(116, \cdot)\)	n/a	480	4
2475.2.bt	\(\chi_{2475}(694, \cdot)\)	n/a	496	4
2475.2.bw	\(\chi_{2475}(134, \cdot)\)	n/a	480	4
2475.2.bz	\(\chi_{2475}(809, \cdot)\)	n/a	480	4
2475.2.ca	\(\chi_{2475}(899, \cdot)\)	n/a	288	4
2475.2.cc	\(\chi_{2475}(359, \cdot)\)	n/a	480	4
2475.2.cd	\(\chi_{2475}(289, \cdot)\)	n/a	592	4
2475.2.cf	\(\chi_{2475}(874, \cdot)\)	n/a	352	4
2475.2.cg	\(\chi_{2475}(64, \cdot)\)	n/a	592	4
2475.2.cj	\(\chi_{2475}(559, \cdot)\)	n/a	592	4
2475.2.cm	\(\chi_{2475}(494, \cdot)\)	n/a	480	4
2475.2.co	\(\chi_{2475}(161, \cdot)\)	n/a	480	4
2475.2.cq	\(\chi_{2475}(518, \cdot)\)	n/a	720	4
2475.2.ct	\(\chi_{2475}(43, \cdot)\)	n/a	848	4
2475.2.cu	\(\chi_{2475}(31, \cdot)\)	n/a	2848	8
2475.2.cv	\(\chi_{2475}(166, \cdot)\)	n/a	2400	8
2475.2.cw	\(\chi_{2475}(196, \cdot)\)	n/a	2848	8
2475.2.cx	\(\chi_{2475}(421, \cdot)\)	n/a	2848	8
2475.2.cy	\(\chi_{2475}(301, \cdot)\)	n/a	1776	8
2475.2.cz	\(\chi_{2475}(16, \cdot)\)	n/a	2848	8
2475.2.da	\(\chi_{2475}(323, \cdot)\)	n/a	960	8
2475.2.dd	\(\chi_{2475}(28, \cdot)\)	n/a	1184	8
2475.2.de	\(\chi_{2475}(127, \cdot)\)	n/a	1184	8
2475.2.dk	\(\chi_{2475}(188, \cdot)\)	n/a	800	8
2475.2.dl	\(\chi_{2475}(368, \cdot)\)	n/a	576	8
2475.2.dm	\(\chi_{2475}(53, \cdot)\)	n/a	960	8
2475.2.dn	\(\chi_{2475}(152, \cdot)\)	n/a	960	8
2475.2.do	\(\chi_{2475}(118, \cdot)\)	n/a	704	8
2475.2.dp	\(\chi_{2475}(1063, \cdot)\)	n/a	1184	8
2475.2.dq	\(\chi_{2475}(172, \cdot)\)	n/a	1184	8
2475.2.dr	\(\chi_{2475}(208, \cdot)\)	n/a	1184	8
2475.2.dx	\(\chi_{2475}(278, \cdot)\)	n/a	960	8
2475.2.dy	\(\chi_{2475}(41, \cdot)\)	n/a	2848	8
2475.2.ec	\(\chi_{2475}(164, \cdot)\)	n/a	2848	8
2475.2.ed	\(\chi_{2475}(169, \cdot)\)	n/a	2848	8
2475.2.ef	\(\chi_{2475}(4, \cdot)\)	n/a	2848	8
2475.2.eg	\(\chi_{2475}(49, \cdot)\)	n/a	1696	8
2475.2.ej	\(\chi_{2475}(229, \cdot)\)	n/a	2848	8
2475.2.em	\(\chi_{2475}(239, \cdot)\)	n/a	2848	8
2475.2.ep	\(\chi_{2475}(74, \cdot)\)	n/a	1696	8
2475.2.eq	\(\chi_{2475}(29, \cdot)\)	n/a	2848	8
2475.2.es	\(\chi_{2475}(194, \cdot)\)	n/a	2848	8
2475.2.et	\(\chi_{2475}(34, \cdot)\)	n/a	2400	8
2475.2.ey	\(\chi_{2475}(761, \cdot)\)	n/a	2848	8
2475.2.ez	\(\chi_{2475}(101, \cdot)\)	n/a	1776	8
2475.2.fb	\(\chi_{2475}(266, \cdot)\)	n/a	2848	8
2475.2.fd	\(\chi_{2475}(281, \cdot)\)	n/a	2848	8
2475.2.fj	\(\chi_{2475}(131, \cdot)\)	n/a	2848	8
2475.2.fl	\(\chi_{2475}(394, \cdot)\)	n/a	2848	8
2475.2.fm	\(\chi_{2475}(479, \cdot)\)	n/a	2848	8
2475.2.fp	\(\chi_{2475}(47, \cdot)\)	n/a	5696	16
2475.2.fq	\(\chi_{2475}(277, \cdot)\)	n/a	5696	16
2475.2.fr	\(\chi_{2475}(52, \cdot)\)	n/a	5696	16
2475.2.fs	\(\chi_{2475}(7, \cdot)\)	n/a	3392	16
2475.2.ft	\(\chi_{2475}(142, \cdot)\)	n/a	5696	16
2475.2.gc	\(\chi_{2475}(23, \cdot)\)	n/a	4800	16
2475.2.gd	\(\chi_{2475}(38, \cdot)\)	n/a	5696	16
2475.2.ge	\(\chi_{2475}(488, \cdot)\)	n/a	5696	16
2475.2.gf	\(\chi_{2475}(218, \cdot)\)	n/a	3392	16
2475.2.gg	\(\chi_{2475}(13, \cdot)\)	n/a	5696	16
2475.2.gj	\(\chi_{2475}(502, \cdot)\)	n/a	5696	16
2475.2.gk	\(\chi_{2475}(113, \cdot)\)	n/a	5696	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2475))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2475)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(825))\)\(^{\oplus 2}\)