Space of modular forms of level 1521 and weight 2

• Label: 1521.2
• Level: 1521
• Weight: 2
• Dimension: 65715
• Nonzero newspaces: 30
• Sturm bound: 340704
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1521 = 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(340704\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1521))\).

	Total	New	Old
Modular forms	87000	67556	19444
Cusp forms	83353	65715	17638
Eisenstein series	3647	1841	1806

Trace form

65715 * q - 198 * q^2 - 264 * q^3 - 198 * q^4 - 198 * q^5 - 264 * q^6 - 194 * q^7 - 180 * q^8 - 264 * q^9 - 564 * q^10 - 186 * q^11 - 264 * q^12 - 204 * q^13 - 354 * q^14 - 264 * q^15 - 158 * q^16 - 180 * q^17 - 264 * q^18 - 554 * q^19 - 132 * q^20 - 264 * q^21 - 138 * q^22 - 174 * q^23 - 312 * q^24 - 156 * q^25 - 186 * q^26 - 504 * q^27 - 558 * q^28 - 240 * q^29 - 360 * q^30 - 258 * q^31 - 354 * q^32 - 336 * q^33 - 294 * q^34 - 354 * q^35 - 456 * q^36 - 672 * q^37 - 450 * q^38 - 336 * q^39 - 618 * q^40 - 300 * q^41 - 408 * q^42 - 218 * q^43 - 426 * q^44 - 384 * q^45 - 618 * q^46 - 258 * q^47 - 408 * q^48 - 194 * q^49 - 300 * q^50 - 312 * q^51 - 165 * q^52 - 282 * q^53 - 264 * q^54 - 462 * q^55 - 162 * q^56 - 264 * q^57 - 48 * q^58 - 114 * q^59 - 384 * q^60 - 84 * q^61 - 174 * q^62 - 360 * q^63 - 636 * q^64 - 279 * q^65 - 744 * q^66 - 278 * q^67 - 576 * q^68 - 408 * q^69 - 498 * q^70 - 462 * q^71 - 576 * q^72 - 842 * q^73 - 624 * q^74 - 504 * q^75 - 494 * q^76 - 450 * q^77 - 516 * q^78 - 450 * q^79 - 816 * q^80 - 456 * q^81 - 852 * q^82 - 522 * q^83 - 600 * q^84 - 396 * q^85 - 570 * q^86 - 456 * q^87 - 426 * q^88 - 294 * q^89 - 576 * q^90 - 646 * q^91 - 570 * q^92 - 408 * q^93 - 198 * q^94 - 174 * q^95 + 48 * q^96 - 78 * q^97 - 150 * q^98 - 120 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1521))\)

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
1521.2.a	\(\chi_{1521}(1, \cdot)\)	1521.2.a.a	1	1
		1521.2.a.b	1
		1521.2.a.c	1
		1521.2.a.d	1
		1521.2.a.e	1
		1521.2.a.f	2
		1521.2.a.g	2
		1521.2.a.h	2
		1521.2.a.i	2
		1521.2.a.j	2
		1521.2.a.k	2
		1521.2.a.l	2
		1521.2.a.m	2
		1521.2.a.n	3
		1521.2.a.o	3
		1521.2.a.p	3
		1521.2.a.q	3
		1521.2.a.r	3
		1521.2.a.s	3
		1521.2.a.t	4
		1521.2.a.u	4
		1521.2.a.v	6
		1521.2.a.w	6
1521.2.b	\(\chi_{1521}(1351, \cdot)\)	1521.2.b.a	2	1
		1521.2.b.b	2
		1521.2.b.c	2
		1521.2.b.d	2
		1521.2.b.e	2
		1521.2.b.f	2
		1521.2.b.g	4
		1521.2.b.h	4
		1521.2.b.i	4
		1521.2.b.j	4
		1521.2.b.k	6
		1521.2.b.l	6
		1521.2.b.m	6
		1521.2.b.n	12
1521.2.e	\(\chi_{1521}(508, \cdot)\)	n/a	288	2
1521.2.f	\(\chi_{1521}(529, \cdot)\)	n/a	288	2
1521.2.g	\(\chi_{1521}(991, \cdot)\)	n/a	120	2
1521.2.h	\(\chi_{1521}(22, \cdot)\)	n/a	288	2
1521.2.i	\(\chi_{1521}(746, \cdot)\)	1521.2.i.a	4	2
		1521.2.i.b	4
		1521.2.i.c	8
		1521.2.i.d	8
		1521.2.i.e	8
		1521.2.i.f	8
		1521.2.i.g	12
		1521.2.i.h	48
1521.2.l	\(\chi_{1521}(823, \cdot)\)	n/a	288	2
1521.2.q	\(\chi_{1521}(316, \cdot)\)	n/a	118	2
1521.2.r	\(\chi_{1521}(868, \cdot)\)	n/a	288	2
1521.2.t	\(\chi_{1521}(337, \cdot)\)	n/a	288	2
1521.2.x	\(\chi_{1521}(587, \cdot)\)	n/a	576	4
1521.2.z	\(\chi_{1521}(239, \cdot)\)	n/a	576	4
1521.2.ba	\(\chi_{1521}(80, \cdot)\)	n/a	208	4
1521.2.bc	\(\chi_{1521}(488, \cdot)\)	n/a	576	4
1521.2.be	\(\chi_{1521}(118, \cdot)\)	n/a	900	12
1521.2.bh	\(\chi_{1521}(64, \cdot)\)	n/a	912	12
1521.2.bi	\(\chi_{1521}(16, \cdot)\)	n/a	4320	24
1521.2.bj	\(\chi_{1521}(55, \cdot)\)	n/a	1776	24
1521.2.bk	\(\chi_{1521}(61, \cdot)\)	n/a	4320	24
1521.2.bl	\(\chi_{1521}(40, \cdot)\)	n/a	4320	24
1521.2.bn	\(\chi_{1521}(8, \cdot)\)	n/a	1488	24
1521.2.bq	\(\chi_{1521}(25, \cdot)\)	n/a	4320	24
1521.2.bs	\(\chi_{1521}(43, \cdot)\)	n/a	4320	24
1521.2.bt	\(\chi_{1521}(10, \cdot)\)	n/a	1800	24
1521.2.by	\(\chi_{1521}(4, \cdot)\)	n/a	4320	24
1521.2.cb	\(\chi_{1521}(20, \cdot)\)	n/a	8640	48
1521.2.cd	\(\chi_{1521}(71, \cdot)\)	n/a	2880	48
1521.2.ce	\(\chi_{1521}(5, \cdot)\)	n/a	8640	48
1521.2.cg	\(\chi_{1521}(2, \cdot)\)	n/a	8640	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1521))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1521)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)