Space of modular forms of level 1521 and weight 4

• Label: 1521.4
• Level: 1521
• Weight: 4
• Dimension: 198986
• Nonzero newspaces: 30
• Sturm bound: 681408
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1521 = 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(681408\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1521))\).

	Total	New	Old
Modular forms	257352	200827	56525
Cusp forms	253704	198986	54718
Eisenstein series	3648	1841	1807

Trace form

198986 * q - 201 * q^2 - 267 * q^3 - 211 * q^4 - 213 * q^5 - 255 * q^6 - 113 * q^7 + 12 * q^8 - 219 * q^9 - 762 * q^10 - 384 * q^11 - 420 * q^12 - 360 * q^13 - 678 * q^14 - 237 * q^15 - 127 * q^16 + 378 * q^17 - 48 * q^18 + 196 * q^19 + 846 * q^20 - 243 * q^21 - 945 * q^22 - 687 * q^23 - 555 * q^24 - 940 * q^25 - 966 * q^26 - 936 * q^27 - 4922 * q^28 - 4281 * q^29 - 3240 * q^30 - 1325 * q^31 + 381 * q^32 + 510 * q^33 + 4353 * q^34 + 6048 * q^35 + 5655 * q^36 + 3082 * q^37 + 8535 * q^38 + 1536 * q^39 + 13614 * q^40 + 6756 * q^41 + 2994 * q^42 + 2050 * q^43 + 1944 * q^44 - 1419 * q^45 - 6234 * q^46 - 5757 * q^47 - 7773 * q^48 - 9636 * q^49 - 18009 * q^50 - 5631 * q^51 - 4494 * q^52 - 2166 * q^53 + 951 * q^54 - 2148 * q^55 - 5340 * q^56 - 1485 * q^57 - 2190 * q^58 - 1980 * q^59 - 3300 * q^60 + 1807 * q^61 - 18210 * q^62 - 12429 * q^63 - 23428 * q^64 - 7533 * q^65 - 14694 * q^66 - 6578 * q^67 - 11655 * q^68 + 1347 * q^69 + 7608 * q^70 + 12090 * q^71 + 15291 * q^72 + 17254 * q^73 + 37518 * q^74 + 16413 * q^75 + 40171 * q^76 + 28731 * q^77 + 17268 * q^78 + 17629 * q^79 + 57582 * q^80 + 11649 * q^81 + 23280 * q^82 + 14685 * q^83 + 12138 * q^84 + 5238 * q^85 + 8493 * q^86 - 2913 * q^87 - 19551 * q^88 - 9390 * q^89 - 25668 * q^90 - 8004 * q^91 - 53760 * q^92 - 23949 * q^93 - 55026 * q^94 - 40122 * q^95 + 6312 * q^96 - 16448 * q^97 + 9636 * q^98 + 27393 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1521))\)

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
1521.4.a	\(\chi_{1521}(1, \cdot)\)	1521.4.a.a	1	1
		1521.4.a.b	1
		1521.4.a.c	1
		1521.4.a.d	1
		1521.4.a.e	1
		1521.4.a.f	1
		1521.4.a.g	1
		1521.4.a.h	1
		1521.4.a.i	1
		1521.4.a.j	1
		1521.4.a.k	1
		1521.4.a.l	2
		1521.4.a.m	2
		1521.4.a.n	2
		1521.4.a.o	2
		1521.4.a.p	2
		1521.4.a.q	2
		1521.4.a.r	2
		1521.4.a.s	2
		1521.4.a.t	2
		1521.4.a.u	3
		1521.4.a.v	4
		1521.4.a.w	4
		1521.4.a.x	4
		1521.4.a.y	4
		1521.4.a.z	4
		1521.4.a.ba	4
		1521.4.a.bb	4
		1521.4.a.bc	8
		1521.4.a.bd	8
		1521.4.a.be	9
		1521.4.a.bf	9
		1521.4.a.bg	9
		1521.4.a.bh	9
		1521.4.a.bi	9
		1521.4.a.bj	9
		1521.4.a.bk	10
		1521.4.a.bl	12
		1521.4.a.bm	18
		1521.4.a.bn	18
1521.4.b	\(\chi_{1521}(1351, \cdot)\)	n/a	188	1
1521.4.e	\(\chi_{1521}(508, \cdot)\)	n/a	908	2
1521.4.f	\(\chi_{1521}(529, \cdot)\)	n/a	904	2
1521.4.g	\(\chi_{1521}(991, \cdot)\)	n/a	374	2
1521.4.h	\(\chi_{1521}(22, \cdot)\)	n/a	904	2
1521.4.i	\(\chi_{1521}(746, \cdot)\)	n/a	308	2
1521.4.l	\(\chi_{1521}(823, \cdot)\)	n/a	904	2
1521.4.q	\(\chi_{1521}(316, \cdot)\)	n/a	376	2
1521.4.r	\(\chi_{1521}(868, \cdot)\)	n/a	904	2
1521.4.t	\(\chi_{1521}(337, \cdot)\)	n/a	904	2
1521.4.x	\(\chi_{1521}(587, \cdot)\)	n/a	1808	4
1521.4.z	\(\chi_{1521}(239, \cdot)\)	n/a	1808	4
1521.4.ba	\(\chi_{1521}(80, \cdot)\)	n/a	616	4
1521.4.bc	\(\chi_{1521}(488, \cdot)\)	n/a	1808	4
1521.4.be	\(\chi_{1521}(118, \cdot)\)	n/a	2724	12
1521.4.bh	\(\chi_{1521}(64, \cdot)\)	n/a	2712	12
1521.4.bi	\(\chi_{1521}(16, \cdot)\)	n/a	13056	24
1521.4.bj	\(\chi_{1521}(55, \cdot)\)	n/a	5448	24
1521.4.bk	\(\chi_{1521}(61, \cdot)\)	n/a	13056	24
1521.4.bl	\(\chi_{1521}(40, \cdot)\)	n/a	13056	24
1521.4.bn	\(\chi_{1521}(8, \cdot)\)	n/a	4368	24
1521.4.bq	\(\chi_{1521}(25, \cdot)\)	n/a	13056	24
1521.4.bs	\(\chi_{1521}(43, \cdot)\)	n/a	13056	24
1521.4.bt	\(\chi_{1521}(10, \cdot)\)	n/a	5424	24
1521.4.by	\(\chi_{1521}(4, \cdot)\)	n/a	13056	24
1521.4.cb	\(\chi_{1521}(20, \cdot)\)	n/a	26112	48
1521.4.cd	\(\chi_{1521}(71, \cdot)\)	n/a	8736	48
1521.4.ce	\(\chi_{1521}(5, \cdot)\)	n/a	26112	48
1521.4.cg	\(\chi_{1521}(2, \cdot)\)	n/a	26112	48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1521))\) into lower level spaces

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