Space of modular forms of level 1575 and weight 2

• Label: 1575.2
• Level: 1575
• Weight: 2
• Dimension: 59493
• Nonzero newspaces: 60
• Sturm bound: 345600
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(345600\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1575))\).

	Total	New	Old
Modular forms	89088	61337	27751
Cusp forms	83713	59493	24220
Eisenstein series	5375	1844	3531

Trace form

59493 * q - 85 * q^2 - 108 * q^3 - 105 * q^4 - 102 * q^5 - 172 * q^6 - 115 * q^7 - 195 * q^8 - 92 * q^9 - 282 * q^10 - 106 * q^11 - 32 * q^12 - 72 * q^13 - 57 * q^14 - 296 * q^15 - 65 * q^16 - 8 * q^17 + 12 * q^18 - 200 * q^19 + 36 * q^20 - 162 * q^21 - 44 * q^22 + 46 * q^23 + 104 * q^24 - 6 * q^25 - 24 * q^26 + 6 * q^27 - 95 * q^28 + 2 * q^29 - 48 * q^30 - 26 * q^31 + 257 * q^32 - 20 * q^33 + 190 * q^34 - 76 * q^35 - 428 * q^36 - 68 * q^37 + 98 * q^38 - 168 * q^39 + 42 * q^40 - 124 * q^41 - 122 * q^42 - 164 * q^43 - 18 * q^44 - 168 * q^45 - 184 * q^46 - 86 * q^47 - 328 * q^48 - 35 * q^49 - 110 * q^50 - 332 * q^51 + 284 * q^52 + 8 * q^53 - 122 * q^54 - 124 * q^55 - 105 * q^56 - 216 * q^57 + 352 * q^58 + 148 * q^59 - 232 * q^60 + 74 * q^61 + 88 * q^62 - 180 * q^63 - 531 * q^64 - 178 * q^65 - 38 * q^66 - 12 * q^67 - 488 * q^68 - 140 * q^69 - 114 * q^70 - 152 * q^71 - 594 * q^72 - 186 * q^73 - 440 * q^74 - 448 * q^75 - 138 * q^76 - 162 * q^77 - 756 * q^78 - 108 * q^79 - 1030 * q^80 - 344 * q^81 - 406 * q^82 - 514 * q^83 - 644 * q^84 - 282 * q^85 - 634 * q^86 - 506 * q^87 - 450 * q^88 - 690 * q^89 - 752 * q^90 - 704 * q^91 - 1312 * q^92 - 578 * q^93 - 230 * q^94 - 292 * q^95 - 1016 * q^96 - 136 * q^97 - 975 * q^98 - 600 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1575))\)

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
1575.2.a	\(\chi_{1575}(1, \cdot)\)	1575.2.a.a	1	1
		1575.2.a.b	1
		1575.2.a.c	1
		1575.2.a.d	1
		1575.2.a.e	1
		1575.2.a.f	1
		1575.2.a.g	1
		1575.2.a.h	1
		1575.2.a.i	1
		1575.2.a.j	1
		1575.2.a.k	1
		1575.2.a.l	2
		1575.2.a.m	2
		1575.2.a.n	2
		1575.2.a.o	2
		1575.2.a.p	2
		1575.2.a.q	2
		1575.2.a.r	2
		1575.2.a.s	2
		1575.2.a.t	2
		1575.2.a.u	2
		1575.2.a.v	2
		1575.2.a.w	3
		1575.2.a.x	3
		1575.2.a.y	4
		1575.2.a.z	4
1575.2.b	\(\chi_{1575}(251, \cdot)\)	1575.2.b.a	4	1
		1575.2.b.b	4
		1575.2.b.c	4
		1575.2.b.d	4
		1575.2.b.e	4
		1575.2.b.f	8
		1575.2.b.g	8
		1575.2.b.h	16
1575.2.d	\(\chi_{1575}(1324, \cdot)\)	1575.2.d.a	2	1
		1575.2.d.b	2
		1575.2.d.c	2
		1575.2.d.d	4
		1575.2.d.e	4
		1575.2.d.f	4
		1575.2.d.g	4
		1575.2.d.h	4
		1575.2.d.i	4
		1575.2.d.j	4
		1575.2.d.k	4
		1575.2.d.l	8
1575.2.g	\(\chi_{1575}(1574, \cdot)\)	1575.2.g.a	8	1
		1575.2.g.b	8
		1575.2.g.c	8
		1575.2.g.d	8
		1575.2.g.e	16
1575.2.i	\(\chi_{1575}(526, \cdot)\)	n/a	228	2
1575.2.j	\(\chi_{1575}(226, \cdot)\)	n/a	120	2
1575.2.k	\(\chi_{1575}(1201, \cdot)\)	n/a	292	2
1575.2.l	\(\chi_{1575}(151, \cdot)\)	n/a	292	2
1575.2.m	\(\chi_{1575}(1268, \cdot)\)	1575.2.m.a	8	2
		1575.2.m.b	8
		1575.2.m.c	12
		1575.2.m.d	12
		1575.2.m.e	16
		1575.2.m.f	16
1575.2.p	\(\chi_{1575}(118, \cdot)\)	n/a	116	2
1575.2.q	\(\chi_{1575}(316, \cdot)\)	n/a	304	4
1575.2.s	\(\chi_{1575}(499, \cdot)\)	n/a	280	2
1575.2.u	\(\chi_{1575}(101, \cdot)\)	n/a	292	2
1575.2.v	\(\chi_{1575}(299, \cdot)\)	n/a	280	2
1575.2.ba	\(\chi_{1575}(524, \cdot)\)	n/a	280	2
1575.2.bc	\(\chi_{1575}(899, \cdot)\)	1575.2.bc.a	8	2
		1575.2.bc.b	8
		1575.2.bc.c	24
		1575.2.bc.d	24
		1575.2.bc.e	32
1575.2.bf	\(\chi_{1575}(551, \cdot)\)	n/a	292	2
1575.2.bg	\(\chi_{1575}(424, \cdot)\)	n/a	116	2
1575.2.bi	\(\chi_{1575}(274, \cdot)\)	n/a	216	2
1575.2.bk	\(\chi_{1575}(26, \cdot)\)	1575.2.bk.a	4	2
		1575.2.bk.b	4
		1575.2.bk.c	4
		1575.2.bk.d	8
		1575.2.bk.e	12
		1575.2.bk.f	12
		1575.2.bk.g	16
		1575.2.bk.h	16
		1575.2.bk.i	24
1575.2.bm	\(\chi_{1575}(776, \cdot)\)	n/a	292	2
1575.2.bp	\(\chi_{1575}(949, \cdot)\)	n/a	280	2
1575.2.br	\(\chi_{1575}(824, \cdot)\)	n/a	280	2
1575.2.bu	\(\chi_{1575}(314, \cdot)\)	n/a	320	4
1575.2.bx	\(\chi_{1575}(64, \cdot)\)	n/a	296	4
1575.2.bz	\(\chi_{1575}(566, \cdot)\)	n/a	320	4
1575.2.ca	\(\chi_{1575}(418, \cdot)\)	n/a	560	4
1575.2.cd	\(\chi_{1575}(893, \cdot)\)	n/a	560	4
1575.2.cf	\(\chi_{1575}(32, \cdot)\)	n/a	560	4
1575.2.ch	\(\chi_{1575}(82, \cdot)\)	n/a	232	4
1575.2.cj	\(\chi_{1575}(643, \cdot)\)	n/a	560	4
1575.2.ck	\(\chi_{1575}(218, \cdot)\)	n/a	432	4
1575.2.cm	\(\chi_{1575}(107, \cdot)\)	n/a	192	4
1575.2.co	\(\chi_{1575}(157, \cdot)\)	n/a	560	4
1575.2.cq	\(\chi_{1575}(121, \cdot)\)	n/a	1888	8
1575.2.cr	\(\chi_{1575}(16, \cdot)\)	n/a	1888	8
1575.2.cs	\(\chi_{1575}(46, \cdot)\)	n/a	784	8
1575.2.ct	\(\chi_{1575}(106, \cdot)\)	n/a	1440	8
1575.2.cu	\(\chi_{1575}(433, \cdot)\)	n/a	784	8
1575.2.cx	\(\chi_{1575}(8, \cdot)\)	n/a	480	8
1575.2.cz	\(\chi_{1575}(164, \cdot)\)	n/a	1888	8
1575.2.db	\(\chi_{1575}(4, \cdot)\)	n/a	1888	8
1575.2.de	\(\chi_{1575}(41, \cdot)\)	n/a	1888	8
1575.2.dg	\(\chi_{1575}(206, \cdot)\)	n/a	640	8
1575.2.di	\(\chi_{1575}(169, \cdot)\)	n/a	1440	8
1575.2.dk	\(\chi_{1575}(109, \cdot)\)	n/a	784	8
1575.2.dl	\(\chi_{1575}(236, \cdot)\)	n/a	1888	8
1575.2.do	\(\chi_{1575}(89, \cdot)\)	n/a	640	8
1575.2.dq	\(\chi_{1575}(104, \cdot)\)	n/a	1888	8
1575.2.dv	\(\chi_{1575}(59, \cdot)\)	n/a	1888	8
1575.2.dw	\(\chi_{1575}(131, \cdot)\)	n/a	1888	8
1575.2.dy	\(\chi_{1575}(184, \cdot)\)	n/a	1888	8
1575.2.eb	\(\chi_{1575}(187, \cdot)\)	n/a	3776	16
1575.2.ed	\(\chi_{1575}(53, \cdot)\)	n/a	1280	16
1575.2.ef	\(\chi_{1575}(92, \cdot)\)	n/a	2880	16
1575.2.eg	\(\chi_{1575}(13, \cdot)\)	n/a	3776	16
1575.2.ei	\(\chi_{1575}(73, \cdot)\)	n/a	1568	16
1575.2.ek	\(\chi_{1575}(2, \cdot)\)	n/a	3776	16
1575.2.em	\(\chi_{1575}(23, \cdot)\)	n/a	3776	16
1575.2.ep	\(\chi_{1575}(52, \cdot)\)	n/a	3776	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1575))\) into lower level spaces

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