Space of modular forms of level 900 and weight 4

• Label: 900.4
• Level: 900
• Weight: 4
• Dimension: 27396
• Nonzero newspaces: 24
• Sturm bound: 172800
• Trace bound: 16

Defining parameters

Level:	\( N \)	=	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(172800\)
Trace bound:			\(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(900))\).

	Total	New	Old
Modular forms	65920	27764	38156
Cusp forms	63680	27396	36284
Eisenstein series	2240	368	1872

Trace form

27396 * q - 21 * q^2 - 3 * q^3 - 11 * q^4 - 67 * q^5 - 19 * q^6 + 34 * q^7 + 66 * q^8 - 131 * q^9 + 119 * q^11 - 30 * q^12 + 156 * q^13 - 84 * q^14 + 168 * q^15 - 143 * q^16 + 12 * q^17 - 80 * q^18 - 134 * q^19 + 170 * q^20 - 86 * q^21 + 521 * q^22 + 386 * q^23 + 35 * q^24 + 303 * q^25 - 1324 * q^26 - 456 * q^27 - 1406 * q^28 - 1600 * q^29 - 1192 * q^30 - 1512 * q^31 - 1751 * q^32 - 455 * q^33 - 1185 * q^34 - 28 * q^35 + 1815 * q^36 + 717 * q^37 + 4847 * q^38 + 796 * q^39 + 2780 * q^40 + 1295 * q^41 + 2220 * q^42 + 1845 * q^43 - 1360 * q^44 - 824 * q^45 - 2862 * q^46 - 382 * q^47 - 5267 * q^48 + 449 * q^49 - 4702 * q^50 - 1359 * q^51 - 2952 * q^52 - 4627 * q^53 - 29 * q^54 - 3572 * q^55 + 2968 * q^56 - 3 * q^57 + 7150 * q^58 + 1381 * q^59 + 3508 * q^60 - 7310 * q^61 + 13296 * q^62 + 3120 * q^63 + 11758 * q^64 + 2139 * q^65 + 4978 * q^66 + 991 * q^67 + 6463 * q^68 - 260 * q^69 - 66 * q^70 + 5664 * q^71 - 10501 * q^72 + 4000 * q^73 - 19530 * q^74 - 13832 * q^75 - 2051 * q^76 - 7314 * q^77 - 8276 * q^78 - 1016 * q^79 - 3182 * q^80 + 3929 * q^81 - 12220 * q^82 + 5704 * q^83 + 11550 * q^84 + 3989 * q^85 + 2843 * q^86 + 11966 * q^87 - 15451 * q^88 + 16447 * q^89 + 13496 * q^90 - 8200 * q^91 + 10826 * q^92 + 15040 * q^93 - 3214 * q^94 + 1052 * q^95 + 9596 * q^96 - 13113 * q^97 + 9890 * q^98 + 2722 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(900))\)

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
900.4.a	\(\chi_{900}(1, \cdot)\)	900.4.a.a	1	1
		900.4.a.b	1
		900.4.a.c	1
		900.4.a.d	1
		900.4.a.e	1
		900.4.a.f	1
		900.4.a.g	1
		900.4.a.h	1
		900.4.a.i	1
		900.4.a.j	1
		900.4.a.k	1
		900.4.a.l	1
		900.4.a.m	1
		900.4.a.n	1
		900.4.a.o	1
		900.4.a.p	1
		900.4.a.q	1
		900.4.a.r	1
		900.4.a.s	2
		900.4.a.t	4
900.4.d	\(\chi_{900}(649, \cdot)\)	900.4.d.a	2	1
		900.4.d.b	2
		900.4.d.c	2
		900.4.d.d	2
		900.4.d.e	2
		900.4.d.f	2
		900.4.d.g	2
		900.4.d.h	2
		900.4.d.i	2
		900.4.d.j	2
		900.4.d.k	2
900.4.e	\(\chi_{900}(251, \cdot)\)	n/a	114	1
900.4.h	\(\chi_{900}(899, \cdot)\)	n/a	108	1
900.4.i	\(\chi_{900}(301, \cdot)\)	n/a	114	2
900.4.j	\(\chi_{900}(557, \cdot)\)	900.4.j.a	8	2
		900.4.j.b	12
		900.4.j.c	16
900.4.k	\(\chi_{900}(307, \cdot)\)	n/a	266	2
900.4.n	\(\chi_{900}(181, \cdot)\)	n/a	148	4
900.4.o	\(\chi_{900}(299, \cdot)\)	n/a	640	2
900.4.r	\(\chi_{900}(551, \cdot)\)	n/a	672	2
900.4.s	\(\chi_{900}(49, \cdot)\)	n/a	108	2
900.4.v	\(\chi_{900}(71, \cdot)\)	n/a	720	4
900.4.w	\(\chi_{900}(109, \cdot)\)	n/a	152	4
900.4.z	\(\chi_{900}(179, \cdot)\)	n/a	720	4
900.4.be	\(\chi_{900}(257, \cdot)\)	n/a	216	4
900.4.bf	\(\chi_{900}(7, \cdot)\)	n/a	1280	4
900.4.bg	\(\chi_{900}(61, \cdot)\)	n/a	720	8
900.4.bj	\(\chi_{900}(127, \cdot)\)	n/a	1784	8
900.4.bk	\(\chi_{900}(17, \cdot)\)	n/a	240	8
900.4.bn	\(\chi_{900}(59, \cdot)\)	n/a	4288	8
900.4.bq	\(\chi_{900}(169, \cdot)\)	n/a	720	8
900.4.br	\(\chi_{900}(11, \cdot)\)	n/a	4288	8
900.4.bs	\(\chi_{900}(67, \cdot)\)	n/a	8576	16
900.4.bt	\(\chi_{900}(77, \cdot)\)	n/a	1440	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(900))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(900)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 27}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 2}\)