Space of modular forms of level 900 and weight 2

• Label: 900.2
• Level: 900
• Weight: 2
• Dimension: 9010
• Nonzero newspaces: 24
• Newform subspaces: 96
• Sturm bound: 86400
• Trace bound: 16

Defining parameters

Level:	\( N \)	=	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 96 \)
Sturm bound:			\(86400\)
Trace bound:			\(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(900))\).

	Total	New	Old
Modular forms	22720	9378	13342
Cusp forms	20481	9010	11471
Eisenstein series	2239	368	1871

Trace form

9010 * q - 21 * q^2 - 27 * q^4 - 47 * q^5 - 43 * q^6 - 7 * q^7 - 30 * q^8 - 68 * q^9 - 80 * q^10 - 35 * q^11 - 18 * q^12 - 83 * q^13 + 6 * q^14 - 12 * q^15 - 15 * q^16 - 90 * q^17 + 10 * q^18 - 44 * q^19 + 10 * q^20 - 83 * q^21 + 45 * q^22 + 19 * q^23 + 35 * q^24 - 57 * q^25 + 52 * q^26 + 48 * q^27 + 58 * q^28 + 55 * q^29 + 8 * q^30 + 43 * q^31 + 89 * q^32 + 31 * q^33 + 93 * q^34 + 52 * q^35 - 9 * q^36 - 81 * q^37 + 61 * q^38 + 109 * q^39 + 60 * q^40 + 49 * q^41 - 18 * q^42 + 37 * q^43 + 40 * q^44 + 16 * q^45 - 58 * q^46 + 133 * q^47 - 35 * q^48 + 110 * q^49 - 2 * q^50 + 96 * q^51 - 52 * q^52 + 229 * q^53 - 89 * q^54 + 48 * q^55 - 184 * q^56 + 102 * q^57 - 96 * q^58 + 137 * q^59 - 92 * q^60 + 149 * q^61 - 180 * q^62 + 105 * q^63 - 210 * q^64 + 159 * q^65 - 176 * q^66 + 107 * q^67 - 253 * q^68 + 109 * q^69 - 66 * q^70 + 24 * q^71 - 253 * q^72 + 34 * q^73 - 234 * q^74 + 88 * q^75 - 55 * q^76 + 201 * q^77 - 308 * q^78 + 105 * q^79 - 142 * q^80 - 220 * q^81 - 20 * q^82 + 35 * q^83 - 330 * q^84 + 179 * q^85 - 221 * q^86 - 133 * q^87 - 3 * q^88 - 7 * q^89 - 184 * q^90 + 22 * q^91 - 314 * q^92 - 191 * q^93 - 40 * q^94 - 68 * q^95 - 316 * q^96 + 159 * q^97 - 482 * q^98 - 215 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(900))\)

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
900.2.a	\(\chi_{900}(1, \cdot)\)	900.2.a.a	1	1
		900.2.a.b	1
		900.2.a.c	1
		900.2.a.d	1
		900.2.a.e	1
		900.2.a.f	1
		900.2.a.g	1
		900.2.a.h	1
900.2.d	\(\chi_{900}(649, \cdot)\)	900.2.d.a	2	1
		900.2.d.b	2
		900.2.d.c	2
		900.2.d.d	2
900.2.e	\(\chi_{900}(251, \cdot)\)	900.2.e.a	2	1
		900.2.e.b	2
		900.2.e.c	2
		900.2.e.d	8
		900.2.e.e	8
		900.2.e.f	8
		900.2.e.g	8
900.2.h	\(\chi_{900}(899, \cdot)\)	900.2.h.a	4	1
		900.2.h.b	8
		900.2.h.c	8
		900.2.h.d	16
900.2.i	\(\chi_{900}(301, \cdot)\)	900.2.i.a	2	2
		900.2.i.b	2
		900.2.i.c	6
		900.2.i.d	8
		900.2.i.e	8
		900.2.i.f	12
900.2.j	\(\chi_{900}(557, \cdot)\)	900.2.j.a	4	2
		900.2.j.b	8
900.2.k	\(\chi_{900}(307, \cdot)\)	900.2.k.a	2	2
		900.2.k.b	2
		900.2.k.c	2
		900.2.k.d	2
		900.2.k.e	2
		900.2.k.f	8
		900.2.k.g	8
		900.2.k.h	8
		900.2.k.i	8
		900.2.k.j	8
		900.2.k.k	8
		900.2.k.l	8
		900.2.k.m	8
		900.2.k.n	12
900.2.n	\(\chi_{900}(181, \cdot)\)	900.2.n.a	8	4
		900.2.n.b	8
		900.2.n.c	12
		900.2.n.d	24
900.2.o	\(\chi_{900}(299, \cdot)\)	900.2.o.a	16	2
		900.2.o.b	48
		900.2.o.c	48
		900.2.o.d	96
900.2.r	\(\chi_{900}(551, \cdot)\)	900.2.r.a	8	2
		900.2.r.b	8
		900.2.r.c	8
		900.2.r.d	48
		900.2.r.e	48
		900.2.r.f	48
		900.2.r.g	48
900.2.s	\(\chi_{900}(49, \cdot)\)	900.2.s.a	4	2
		900.2.s.b	4
		900.2.s.c	12
		900.2.s.d	16
900.2.v	\(\chi_{900}(71, \cdot)\)	900.2.v.a	16	4
		900.2.v.b	224
900.2.w	\(\chi_{900}(109, \cdot)\)	900.2.w.a	8	4
		900.2.w.b	16
		900.2.w.c	24
900.2.z	\(\chi_{900}(179, \cdot)\)	900.2.z.a	16	4
		900.2.z.b	224
900.2.be	\(\chi_{900}(257, \cdot)\)	900.2.be.a	4	4
		900.2.be.b	4
		900.2.be.c	4
		900.2.be.d	4
		900.2.be.e	24
		900.2.be.f	32
900.2.bf	\(\chi_{900}(7, \cdot)\)	900.2.bf.a	8	4
		900.2.bf.b	8
		900.2.bf.c	16
		900.2.bf.d	64
		900.2.bf.e	128
		900.2.bf.f	192
900.2.bg	\(\chi_{900}(61, \cdot)\)	900.2.bg.a	240	8
900.2.bj	\(\chi_{900}(127, \cdot)\)	900.2.bj.a	8	8
		900.2.bj.b	8
		900.2.bj.c	8
		900.2.bj.d	96
		900.2.bj.e	224
		900.2.bj.f	240
900.2.bk	\(\chi_{900}(17, \cdot)\)	900.2.bk.a	80	8
900.2.bn	\(\chi_{900}(59, \cdot)\)	900.2.bn.a	1408	8
900.2.bq	\(\chi_{900}(169, \cdot)\)	900.2.bq.a	240	8
900.2.br	\(\chi_{900}(11, \cdot)\)	900.2.br.a	1408	8
900.2.bs	\(\chi_{900}(67, \cdot)\)	900.2.bs.a	2816	16
900.2.bt	\(\chi_{900}(77, \cdot)\)	900.2.bt.a	480	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(900))\) into lower level spaces

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