Space of modular forms of level 1575 and weight 4

• Label: 1575.4
• Level: 1575
• Weight: 4
• Dimension: 180323
• Nonzero newspaces: 60
• Sturm bound: 691200
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(691200\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1575))\).

	Total	New	Old
Modular forms	261888	182167	79721
Cusp forms	256512	180323	76189
Eisenstein series	5376	1844	3532

Trace form

180323 * q - 83 * q^2 - 102 * q^3 - 15 * q^4 - 102 * q^5 - 190 * q^6 - 72 * q^7 - 93 * q^8 + 58 * q^9 - 52 * q^10 + 19 * q^11 - 260 * q^12 - 728 * q^13 - 411 * q^14 - 656 * q^15 - 1475 * q^16 - 703 * q^17 - 876 * q^18 + 325 * q^19 + 1596 * q^20 + 543 * q^21 + 3066 * q^22 + 2027 * q^23 + 938 * q^24 - 1386 * q^25 - 1398 * q^26 - 1056 * q^27 - 2017 * q^28 - 5120 * q^29 - 2448 * q^30 - 2983 * q^31 - 6425 * q^32 - 4208 * q^33 + 918 * q^34 - 1016 * q^35 - 4346 * q^36 + 3001 * q^37 + 6688 * q^38 + 3258 * q^39 + 7752 * q^40 + 7144 * q^41 + 4456 * q^42 - 616 * q^43 + 11226 * q^44 + 4392 * q^45 - 242 * q^46 + 12623 * q^47 + 16058 * q^48 + 3410 * q^49 - 3400 * q^50 + 238 * q^51 - 3162 * q^52 - 8225 * q^53 - 14624 * q^54 - 564 * q^55 + 645 * q^56 - 17214 * q^57 - 3816 * q^58 - 16771 * q^59 - 28072 * q^60 - 14479 * q^61 - 26320 * q^62 - 3519 * q^63 - 23411 * q^64 - 10418 * q^65 + 4354 * q^66 - 5757 * q^67 + 10634 * q^68 + 16234 * q^69 + 2166 * q^70 + 8312 * q^71 + 19968 * q^72 + 26227 * q^73 + 20438 * q^74 + 12992 * q^75 + 21554 * q^76 - 1266 * q^77 - 10704 * q^78 + 7983 * q^79 + 32680 * q^80 - 1154 * q^81 + 14842 * q^82 + 24226 * q^83 - 938 * q^84 + 10298 * q^85 + 16156 * q^86 - 3518 * q^87 - 66348 * q^88 - 26289 * q^89 - 18512 * q^90 - 22236 * q^91 - 30212 * q^92 + 19294 * q^93 - 30636 * q^94 - 4772 * q^95 + 42568 * q^96 - 12520 * q^97 + 47433 * q^98 + 33414 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1575))\)

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
1575.4.a	\(\chi_{1575}(1, \cdot)\)	1575.4.a.a	1	1
		1575.4.a.b	1
		1575.4.a.c	1
		1575.4.a.d	1
		1575.4.a.e	1
		1575.4.a.f	1
		1575.4.a.g	1
		1575.4.a.h	1
		1575.4.a.i	1
		1575.4.a.j	1
		1575.4.a.k	1
		1575.4.a.l	1
		1575.4.a.m	2
		1575.4.a.n	2
		1575.4.a.o	2
		1575.4.a.p	2
		1575.4.a.q	2
		1575.4.a.r	2
		1575.4.a.s	2
		1575.4.a.t	2
		1575.4.a.u	2
		1575.4.a.v	2
		1575.4.a.w	2
		1575.4.a.x	2
		1575.4.a.y	2
		1575.4.a.z	2
		1575.4.a.ba	3
		1575.4.a.bb	3
		1575.4.a.bc	3
		1575.4.a.bd	3
		1575.4.a.be	3
		1575.4.a.bf	4
		1575.4.a.bg	4
		1575.4.a.bh	4
		1575.4.a.bi	4
		1575.4.a.bj	4
		1575.4.a.bk	4
		1575.4.a.bl	4
		1575.4.a.bm	4
		1575.4.a.bn	5
		1575.4.a.bo	5
		1575.4.a.bp	5
		1575.4.a.bq	5
		1575.4.a.br	8
		1575.4.a.bs	8
		1575.4.a.bt	10
		1575.4.a.bu	10
1575.4.b	\(\chi_{1575}(251, \cdot)\)	n/a	152	1
1575.4.d	\(\chi_{1575}(1324, \cdot)\)	n/a	134	1
1575.4.g	\(\chi_{1575}(1574, \cdot)\)	n/a	144	1
1575.4.i	\(\chi_{1575}(526, \cdot)\)	n/a	684	2
1575.4.j	\(\chi_{1575}(226, \cdot)\)	n/a	374	2
1575.4.k	\(\chi_{1575}(1201, \cdot)\)	n/a	900	2
1575.4.l	\(\chi_{1575}(151, \cdot)\)	n/a	900	2
1575.4.m	\(\chi_{1575}(1268, \cdot)\)	n/a	216	2
1575.4.p	\(\chi_{1575}(118, \cdot)\)	n/a	356	2
1575.4.q	\(\chi_{1575}(316, \cdot)\)	n/a	896	4
1575.4.s	\(\chi_{1575}(499, \cdot)\)	n/a	856	2
1575.4.u	\(\chi_{1575}(101, \cdot)\)	n/a	900	2
1575.4.v	\(\chi_{1575}(299, \cdot)\)	n/a	856	2
1575.4.ba	\(\chi_{1575}(524, \cdot)\)	n/a	856	2
1575.4.bc	\(\chi_{1575}(899, \cdot)\)	n/a	288	2
1575.4.bf	\(\chi_{1575}(551, \cdot)\)	n/a	900	2
1575.4.bg	\(\chi_{1575}(424, \cdot)\)	n/a	356	2
1575.4.bi	\(\chi_{1575}(274, \cdot)\)	n/a	648	2
1575.4.bk	\(\chi_{1575}(26, \cdot)\)	n/a	304	2
1575.4.bm	\(\chi_{1575}(776, \cdot)\)	n/a	900	2
1575.4.bp	\(\chi_{1575}(949, \cdot)\)	n/a	856	2
1575.4.br	\(\chi_{1575}(824, \cdot)\)	n/a	856	2
1575.4.bu	\(\chi_{1575}(314, \cdot)\)	n/a	960	4
1575.4.bx	\(\chi_{1575}(64, \cdot)\)	n/a	904	4
1575.4.bz	\(\chi_{1575}(566, \cdot)\)	n/a	960	4
1575.4.ca	\(\chi_{1575}(418, \cdot)\)	n/a	1712	4
1575.4.cd	\(\chi_{1575}(893, \cdot)\)	n/a	1712	4
1575.4.cf	\(\chi_{1575}(32, \cdot)\)	n/a	1712	4
1575.4.ch	\(\chi_{1575}(82, \cdot)\)	n/a	712	4
1575.4.cj	\(\chi_{1575}(643, \cdot)\)	n/a	1712	4
1575.4.ck	\(\chi_{1575}(218, \cdot)\)	n/a	1296	4
1575.4.cm	\(\chi_{1575}(107, \cdot)\)	n/a	576	4
1575.4.co	\(\chi_{1575}(157, \cdot)\)	n/a	1712	4
1575.4.cq	\(\chi_{1575}(121, \cdot)\)	n/a	5728	8
1575.4.cr	\(\chi_{1575}(16, \cdot)\)	n/a	5728	8
1575.4.cs	\(\chi_{1575}(46, \cdot)\)	n/a	2384	8
1575.4.ct	\(\chi_{1575}(106, \cdot)\)	n/a	4320	8
1575.4.cu	\(\chi_{1575}(433, \cdot)\)	n/a	2384	8
1575.4.cx	\(\chi_{1575}(8, \cdot)\)	n/a	1440	8
1575.4.cz	\(\chi_{1575}(164, \cdot)\)	n/a	5728	8
1575.4.db	\(\chi_{1575}(4, \cdot)\)	n/a	5728	8
1575.4.de	\(\chi_{1575}(41, \cdot)\)	n/a	5728	8
1575.4.dg	\(\chi_{1575}(206, \cdot)\)	n/a	1920	8
1575.4.di	\(\chi_{1575}(169, \cdot)\)	n/a	4320	8
1575.4.dk	\(\chi_{1575}(109, \cdot)\)	n/a	2384	8
1575.4.dl	\(\chi_{1575}(236, \cdot)\)	n/a	5728	8
1575.4.do	\(\chi_{1575}(89, \cdot)\)	n/a	1920	8
1575.4.dq	\(\chi_{1575}(104, \cdot)\)	n/a	5728	8
1575.4.dv	\(\chi_{1575}(59, \cdot)\)	n/a	5728	8
1575.4.dw	\(\chi_{1575}(131, \cdot)\)	n/a	5728	8
1575.4.dy	\(\chi_{1575}(184, \cdot)\)	n/a	5728	8
1575.4.eb	\(\chi_{1575}(187, \cdot)\)	n/a	11456	16
1575.4.ed	\(\chi_{1575}(53, \cdot)\)	n/a	3840	16
1575.4.ef	\(\chi_{1575}(92, \cdot)\)	n/a	8640	16
1575.4.eg	\(\chi_{1575}(13, \cdot)\)	n/a	11456	16
1575.4.ei	\(\chi_{1575}(73, \cdot)\)	n/a	4768	16
1575.4.ek	\(\chi_{1575}(2, \cdot)\)	n/a	11456	16
1575.4.em	\(\chi_{1575}(23, \cdot)\)	n/a	11456	16
1575.4.ep	\(\chi_{1575}(52, \cdot)\)	n/a	11456	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1575))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1575)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 2}\)