Space of modular forms of level 2475 and weight 4

• Label: 2475.4
• Level: 2475
• Weight: 4
• Dimension: 463274
• Nonzero newspaces: 84
• Sturm bound: 1728000
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 84 \)
Sturm bound:			\(1728000\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2475))\).

	Total	New	Old
Modular forms	652480	466594	185886
Cusp forms	643520	463274	180246
Eisenstein series	8960	3320	5640

Trace form

463274 * q - 161 * q^2 - 206 * q^3 - 93 * q^4 - 198 * q^5 - 358 * q^6 - 163 * q^7 + 13 * q^8 - 46 * q^9 - 340 * q^10 - 161 * q^11 - 672 * q^12 - 933 * q^13 - 2082 * q^14 - 592 * q^15 - 2041 * q^16 - 721 * q^17 - 644 * q^18 + 976 * q^19 + 1500 * q^20 + 1890 * q^21 + 2520 * q^22 + 3108 * q^23 + 2322 * q^24 - 2154 * q^25 - 3422 * q^26 - 1616 * q^27 - 10322 * q^28 - 7399 * q^29 - 2576 * q^30 - 5527 * q^31 - 10096 * q^32 - 4258 * q^33 + 200 * q^34 + 464 * q^35 - 5002 * q^36 + 5913 * q^37 + 12332 * q^38 + 4714 * q^39 + 9224 * q^40 + 12583 * q^41 + 16776 * q^42 + 8240 * q^43 + 18876 * q^44 + 3944 * q^45 + 698 * q^46 + 11437 * q^47 + 19126 * q^48 - 2463 * q^49 - 6072 * q^50 + 2116 * q^51 - 18560 * q^52 - 12309 * q^53 - 12146 * q^54 - 6798 * q^55 - 42812 * q^56 - 18138 * q^57 - 27142 * q^58 - 29188 * q^59 - 28200 * q^60 - 17405 * q^61 - 40124 * q^62 - 22122 * q^63 - 12657 * q^64 - 3626 * q^65 - 9696 * q^66 + 8152 * q^67 + 24114 * q^68 + 6118 * q^69 + 36660 * q^70 + 4535 * q^71 + 16540 * q^72 + 29725 * q^73 + 35324 * q^74 + 12864 * q^75 + 35186 * q^76 + 17352 * q^77 + 11184 * q^78 + 17103 * q^79 + 30460 * q^80 + 3826 * q^81 + 30195 * q^82 + 25440 * q^83 + 19758 * q^84 + 2138 * q^85 + 38525 * q^86 + 23542 * q^87 + 696 * q^88 + 24430 * q^89 + 1712 * q^90 + 15395 * q^91 + 53088 * q^92 + 33718 * q^93 - 196 * q^94 - 820 * q^95 + 47114 * q^96 - 28828 * q^97 - 7790 * q^98 + 16083 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2475))\)

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
2475.4.a	\(\chi_{2475}(1, \cdot)\)	2475.4.a.a	1	1
		2475.4.a.b	1
		2475.4.a.c	1
		2475.4.a.d	1
		2475.4.a.e	1
		2475.4.a.f	1
		2475.4.a.g	1
		2475.4.a.h	1
		2475.4.a.i	1
		2475.4.a.j	1
		2475.4.a.k	1
		2475.4.a.l	2
		2475.4.a.m	2
		2475.4.a.n	2
		2475.4.a.o	2
		2475.4.a.p	2
		2475.4.a.q	2
		2475.4.a.r	2
		2475.4.a.s	3
		2475.4.a.t	3
		2475.4.a.u	3
		2475.4.a.v	3
		2475.4.a.w	3
		2475.4.a.x	3
		2475.4.a.y	3
		2475.4.a.z	3
		2475.4.a.ba	3
		2475.4.a.bb	4
		2475.4.a.bc	4
		2475.4.a.bd	4
		2475.4.a.be	4
		2475.4.a.bf	5
		2475.4.a.bg	5
		2475.4.a.bh	5
		2475.4.a.bi	5
		2475.4.a.bj	5
		2475.4.a.bk	5
		2475.4.a.bl	5
		2475.4.a.bm	5
		2475.4.a.bn	6
		2475.4.a.bo	7
		2475.4.a.bp	7
		2475.4.a.bq	7
		2475.4.a.br	7
		2475.4.a.bs	7
		2475.4.a.bt	7
		2475.4.a.bu	10
		2475.4.a.bv	10
		2475.4.a.bw	10
		2475.4.a.bx	10
		2475.4.a.by	10
		2475.4.a.bz	16
		2475.4.a.ca	16
2475.4.c	\(\chi_{2475}(199, \cdot)\)	n/a	224	1
2475.4.d	\(\chi_{2475}(2474, \cdot)\)	n/a	216	1
2475.4.f	\(\chi_{2475}(2276, \cdot)\)	n/a	228	1
2475.4.i	\(\chi_{2475}(826, \cdot)\)	n/a	1140	2
2475.4.k	\(\chi_{2475}(307, \cdot)\)	n/a	536	2
2475.4.l	\(\chi_{2475}(782, \cdot)\)	n/a	360	2
2475.4.n	\(\chi_{2475}(361, \cdot)\)	n/a	1792	4
2475.4.o	\(\chi_{2475}(676, \cdot)\)	n/a	1128	4
2475.4.p	\(\chi_{2475}(631, \cdot)\)	n/a	1792	4
2475.4.q	\(\chi_{2475}(181, \cdot)\)	n/a	1792	4
2475.4.r	\(\chi_{2475}(496, \cdot)\)	n/a	1496	4
2475.4.s	\(\chi_{2475}(91, \cdot)\)	n/a	1792	4
2475.4.u	\(\chi_{2475}(626, \cdot)\)	n/a	1356	2
2475.4.w	\(\chi_{2475}(824, \cdot)\)	n/a	1288	2
2475.4.z	\(\chi_{2475}(1024, \cdot)\)	n/a	1080	2
2475.4.ba	\(\chi_{2475}(1304, \cdot)\)	n/a	1440	4
2475.4.bd	\(\chi_{2475}(379, \cdot)\)	n/a	1792	4
2475.4.bf	\(\chi_{2475}(296, \cdot)\)	n/a	1440	4
2475.4.bl	\(\chi_{2475}(1106, \cdot)\)	n/a	1440	4
2475.4.bn	\(\chi_{2475}(611, \cdot)\)	n/a	1440	4
2475.4.bq	\(\chi_{2475}(701, \cdot)\)	n/a	912	4
2475.4.br	\(\chi_{2475}(116, \cdot)\)	n/a	1440	4
2475.4.bt	\(\chi_{2475}(694, \cdot)\)	n/a	1504	4
2475.4.bw	\(\chi_{2475}(134, \cdot)\)	n/a	1440	4
2475.4.bz	\(\chi_{2475}(809, \cdot)\)	n/a	1440	4
2475.4.ca	\(\chi_{2475}(899, \cdot)\)	n/a	864	4
2475.4.cc	\(\chi_{2475}(359, \cdot)\)	n/a	1440	4
2475.4.cd	\(\chi_{2475}(289, \cdot)\)	n/a	1792	4
2475.4.cf	\(\chi_{2475}(874, \cdot)\)	n/a	1072	4
2475.4.cg	\(\chi_{2475}(64, \cdot)\)	n/a	1792	4
2475.4.cj	\(\chi_{2475}(559, \cdot)\)	n/a	1792	4
2475.4.cm	\(\chi_{2475}(494, \cdot)\)	n/a	1440	4
2475.4.co	\(\chi_{2475}(161, \cdot)\)	n/a	1440	4
2475.4.cq	\(\chi_{2475}(518, \cdot)\)	n/a	2160	4
2475.4.ct	\(\chi_{2475}(43, \cdot)\)	n/a	2576	4
2475.4.cu	\(\chi_{2475}(31, \cdot)\)	n/a	8608	8
2475.4.cv	\(\chi_{2475}(166, \cdot)\)	n/a	7200	8
2475.4.cw	\(\chi_{2475}(196, \cdot)\)	n/a	8608	8
2475.4.cx	\(\chi_{2475}(421, \cdot)\)	n/a	8608	8
2475.4.cy	\(\chi_{2475}(301, \cdot)\)	n/a	5424	8
2475.4.cz	\(\chi_{2475}(16, \cdot)\)	n/a	8608	8
2475.4.da	\(\chi_{2475}(323, \cdot)\)	n/a	2880	8
2475.4.dd	\(\chi_{2475}(28, \cdot)\)	n/a	3584	8
2475.4.de	\(\chi_{2475}(127, \cdot)\)	n/a	3584	8
2475.4.dk	\(\chi_{2475}(188, \cdot)\)	n/a	2400	8
2475.4.dl	\(\chi_{2475}(368, \cdot)\)	n/a	1728	8
2475.4.dm	\(\chi_{2475}(53, \cdot)\)	n/a	2880	8
2475.4.dn	\(\chi_{2475}(152, \cdot)\)	n/a	2880	8
2475.4.do	\(\chi_{2475}(118, \cdot)\)	n/a	2144	8
2475.4.dp	\(\chi_{2475}(1063, \cdot)\)	n/a	3584	8
2475.4.dq	\(\chi_{2475}(172, \cdot)\)	n/a	3584	8
2475.4.dr	\(\chi_{2475}(208, \cdot)\)	n/a	3584	8
2475.4.dx	\(\chi_{2475}(278, \cdot)\)	n/a	2880	8
2475.4.dy	\(\chi_{2475}(41, \cdot)\)	n/a	8608	8
2475.4.ec	\(\chi_{2475}(164, \cdot)\)	n/a	8608	8
2475.4.ed	\(\chi_{2475}(169, \cdot)\)	n/a	8608	8
2475.4.ef	\(\chi_{2475}(4, \cdot)\)	n/a	8608	8
2475.4.eg	\(\chi_{2475}(49, \cdot)\)	n/a	5152	8
2475.4.ej	\(\chi_{2475}(229, \cdot)\)	n/a	8608	8
2475.4.em	\(\chi_{2475}(239, \cdot)\)	n/a	8608	8
2475.4.ep	\(\chi_{2475}(74, \cdot)\)	n/a	5152	8
2475.4.eq	\(\chi_{2475}(29, \cdot)\)	n/a	8608	8
2475.4.es	\(\chi_{2475}(194, \cdot)\)	n/a	8608	8
2475.4.et	\(\chi_{2475}(34, \cdot)\)	n/a	7200	8
2475.4.ey	\(\chi_{2475}(761, \cdot)\)	n/a	8608	8
2475.4.ez	\(\chi_{2475}(101, \cdot)\)	n/a	5424	8
2475.4.fb	\(\chi_{2475}(266, \cdot)\)	n/a	8608	8
2475.4.fd	\(\chi_{2475}(281, \cdot)\)	n/a	8608	8
2475.4.fj	\(\chi_{2475}(131, \cdot)\)	n/a	8608	8
2475.4.fl	\(\chi_{2475}(394, \cdot)\)	n/a	8608	8
2475.4.fm	\(\chi_{2475}(479, \cdot)\)	n/a	8608	8
2475.4.fp	\(\chi_{2475}(47, \cdot)\)	n/a	17216	16
2475.4.fq	\(\chi_{2475}(277, \cdot)\)	n/a	17216	16
2475.4.fr	\(\chi_{2475}(52, \cdot)\)	n/a	17216	16
2475.4.fs	\(\chi_{2475}(7, \cdot)\)	n/a	10304	16
2475.4.ft	\(\chi_{2475}(142, \cdot)\)	n/a	17216	16
2475.4.gc	\(\chi_{2475}(23, \cdot)\)	n/a	14400	16
2475.4.gd	\(\chi_{2475}(38, \cdot)\)	n/a	17216	16
2475.4.ge	\(\chi_{2475}(488, \cdot)\)	n/a	17216	16
2475.4.gf	\(\chi_{2475}(218, \cdot)\)	n/a	10304	16
2475.4.gg	\(\chi_{2475}(13, \cdot)\)	n/a	17216	16
2475.4.gj	\(\chi_{2475}(502, \cdot)\)	n/a	17216	16
2475.4.gk	\(\chi_{2475}(113, \cdot)\)	n/a	17216	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2475))\) into lower level spaces

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