Space of modular forms of level 3200 and weight 2

• Label: 3200.2
• Level: 3200
• Weight: 2
• Dimension: 158280
• Nonzero newspaces: 36
• Sturm bound: 1228800
• Trace bound: 33

Defining parameters

Level:	\( N \)	=	\( 3200 = 2^{7} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(1228800\)
Trace bound:			\(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3200))\).

	Total	New	Old
Modular forms	311680	160248	151432
Cusp forms	302721	158280	144441
Eisenstein series	8959	1968	6991

Trace form

158280 * q - 208 * q^2 - 156 * q^3 - 208 * q^4 - 256 * q^5 - 336 * q^6 - 156 * q^7 - 208 * q^8 - 260 * q^9 - 256 * q^10 - 252 * q^11 - 208 * q^12 - 208 * q^13 - 208 * q^14 - 192 * q^15 - 336 * q^16 - 312 * q^17 - 208 * q^18 - 156 * q^19 - 256 * q^20 - 348 * q^21 - 208 * q^22 - 164 * q^23 - 208 * q^24 - 320 * q^25 - 656 * q^26 - 180 * q^27 - 208 * q^28 - 224 * q^29 - 256 * q^30 - 272 * q^31 - 208 * q^32 - 448 * q^33 - 208 * q^34 - 192 * q^35 - 336 * q^36 - 224 * q^37 - 208 * q^38 - 180 * q^39 - 256 * q^40 - 436 * q^41 - 208 * q^42 - 164 * q^43 - 208 * q^44 - 256 * q^45 - 336 * q^46 - 160 * q^47 - 208 * q^48 - 284 * q^49 - 256 * q^50 - 488 * q^51 - 112 * q^52 - 176 * q^53 - 80 * q^54 - 192 * q^55 - 224 * q^56 - 196 * q^57 - 64 * q^58 - 124 * q^59 - 256 * q^60 - 272 * q^61 - 112 * q^62 - 96 * q^63 - 16 * q^64 - 256 * q^65 - 144 * q^66 - 116 * q^67 - 112 * q^68 - 156 * q^69 - 256 * q^70 - 220 * q^71 - 64 * q^72 - 196 * q^73 - 96 * q^74 - 192 * q^75 - 528 * q^76 - 204 * q^77 - 112 * q^78 - 128 * q^79 - 256 * q^80 - 500 * q^81 - 208 * q^82 - 196 * q^83 - 208 * q^84 - 256 * q^85 - 336 * q^86 - 212 * q^87 - 208 * q^88 - 324 * q^89 - 256 * q^90 - 300 * q^91 - 208 * q^92 - 256 * q^93 - 208 * q^94 - 192 * q^95 - 336 * q^96 - 480 * q^97 - 208 * q^98 - 208 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3200))\)

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
3200.2.a	\(\chi_{3200}(1, \cdot)\)	3200.2.a.a	1	1
		3200.2.a.b	1
		3200.2.a.c	1
		3200.2.a.d	1
		3200.2.a.e	1
		3200.2.a.f	1
		3200.2.a.g	1
		3200.2.a.h	1
		3200.2.a.i	1
		3200.2.a.j	1
		3200.2.a.k	1
		3200.2.a.l	1
		3200.2.a.m	1
		3200.2.a.n	1
		3200.2.a.o	1
		3200.2.a.p	1
		3200.2.a.q	1
		3200.2.a.r	1
		3200.2.a.s	1
		3200.2.a.t	1
		3200.2.a.u	1
		3200.2.a.v	1
		3200.2.a.w	1
		3200.2.a.x	1
		3200.2.a.y	1
		3200.2.a.z	1
		3200.2.a.ba	1
		3200.2.a.bb	1
		3200.2.a.bc	2
		3200.2.a.bd	2
		3200.2.a.be	2
		3200.2.a.bf	2
		3200.2.a.bg	2
		3200.2.a.bh	2
		3200.2.a.bi	2
		3200.2.a.bj	2
		3200.2.a.bk	2
		3200.2.a.bl	2
		3200.2.a.bm	2
		3200.2.a.bn	2
		3200.2.a.bo	3
		3200.2.a.bp	3
		3200.2.a.bq	3
		3200.2.a.br	3
		3200.2.a.bs	3
		3200.2.a.bt	3
		3200.2.a.bu	3
		3200.2.a.bv	3
3200.2.c	\(\chi_{3200}(2049, \cdot)\)	3200.2.c.a	2	1
		3200.2.c.b	2
		3200.2.c.c	2
		3200.2.c.d	2
		3200.2.c.e	2
		3200.2.c.f	2
		3200.2.c.g	2
		3200.2.c.h	2
		3200.2.c.i	2
		3200.2.c.j	2
		3200.2.c.k	2
		3200.2.c.l	2
		3200.2.c.m	2
		3200.2.c.n	2
		3200.2.c.o	2
		3200.2.c.p	2
		3200.2.c.q	2
		3200.2.c.r	2
		3200.2.c.s	2
		3200.2.c.t	2
		3200.2.c.u	4
		3200.2.c.v	4
		3200.2.c.w	4
		3200.2.c.x	4
		3200.2.c.y	4
		3200.2.c.z	4
		3200.2.c.ba	4
		3200.2.c.bb	4
3200.2.d	\(\chi_{3200}(1601, \cdot)\)	3200.2.d.a	2	1
		3200.2.d.b	2
		3200.2.d.c	2
		3200.2.d.d	2
		3200.2.d.e	2
		3200.2.d.f	2
		3200.2.d.g	2
		3200.2.d.h	2
		3200.2.d.i	4
		3200.2.d.j	4
		3200.2.d.k	4
		3200.2.d.l	4
		3200.2.d.m	4
		3200.2.d.n	4
		3200.2.d.o	4
		3200.2.d.p	4
		3200.2.d.q	4
		3200.2.d.r	4
		3200.2.d.s	4
		3200.2.d.t	4
		3200.2.d.u	4
		3200.2.d.v	4
		3200.2.d.w	4
3200.2.f	\(\chi_{3200}(449, \cdot)\)	3200.2.f.a	2	1
		3200.2.f.b	2
		3200.2.f.c	2
		3200.2.f.d	2
		3200.2.f.e	2
		3200.2.f.f	2
		3200.2.f.g	4
		3200.2.f.h	4
		3200.2.f.i	4
		3200.2.f.j	4
		3200.2.f.k	4
		3200.2.f.l	4
		3200.2.f.m	4
		3200.2.f.n	4
		3200.2.f.o	4
		3200.2.f.p	4
		3200.2.f.q	4
		3200.2.f.r	8
		3200.2.f.s	8
3200.2.j	\(\chi_{3200}(543, \cdot)\)	n/a	136	2
3200.2.l	\(\chi_{3200}(801, \cdot)\)	n/a	140	2
3200.2.n	\(\chi_{3200}(1407, \cdot)\)	n/a	144	2
3200.2.o	\(\chi_{3200}(1343, \cdot)\)	n/a	144	2
3200.2.q	\(\chi_{3200}(1249, \cdot)\)	n/a	136	2
3200.2.s	\(\chi_{3200}(2143, \cdot)\)	n/a	136	2
3200.2.u	\(\chi_{3200}(641, \cdot)\)	n/a	480	4
3200.2.v	\(\chi_{3200}(143, \cdot)\)	n/a	280	4
3200.2.y	\(\chi_{3200}(401, \cdot)\)	n/a	292	4
3200.2.ba	\(\chi_{3200}(49, \cdot)\)	n/a	280	4
3200.2.bb	\(\chi_{3200}(207, \cdot)\)	n/a	280	4
3200.2.be	\(\chi_{3200}(1089, \cdot)\)	n/a	480	4
3200.2.bg	\(\chi_{3200}(129, \cdot)\)	n/a	480	4
3200.2.bj	\(\chi_{3200}(321, \cdot)\)	n/a	480	4
3200.2.bl	\(\chi_{3200}(407, \cdot)\)	None	0	8
3200.2.bm	\(\chi_{3200}(201, \cdot)\)	None	0	8
3200.2.bn	\(\chi_{3200}(249, \cdot)\)	None	0	8
3200.2.br	\(\chi_{3200}(7, \cdot)\)	None	0	8
3200.2.bt	\(\chi_{3200}(223, \cdot)\)	n/a	928	8
3200.2.bu	\(\chi_{3200}(161, \cdot)\)	n/a	928	8
3200.2.bx	\(\chi_{3200}(63, \cdot)\)	n/a	960	8
3200.2.by	\(\chi_{3200}(127, \cdot)\)	n/a	960	8
3200.2.cb	\(\chi_{3200}(289, \cdot)\)	n/a	928	8
3200.2.cc	\(\chi_{3200}(1183, \cdot)\)	n/a	928	8
3200.2.cf	\(\chi_{3200}(107, \cdot)\)	n/a	4576	16
3200.2.cg	\(\chi_{3200}(101, \cdot)\)	n/a	4816	16
3200.2.ci	\(\chi_{3200}(149, \cdot)\)	n/a	4576	16
3200.2.cl	\(\chi_{3200}(43, \cdot)\)	n/a	4576	16
3200.2.cn	\(\chi_{3200}(47, \cdot)\)	n/a	1888	16
3200.2.co	\(\chi_{3200}(209, \cdot)\)	n/a	1888	16
3200.2.cq	\(\chi_{3200}(81, \cdot)\)	n/a	1888	16
3200.2.ct	\(\chi_{3200}(303, \cdot)\)	n/a	1888	16
3200.2.cu	\(\chi_{3200}(23, \cdot)\)	None	0	32
3200.2.cy	\(\chi_{3200}(9, \cdot)\)	None	0	32
3200.2.cz	\(\chi_{3200}(41, \cdot)\)	None	0	32
3200.2.da	\(\chi_{3200}(87, \cdot)\)	None	0	32
3200.2.dc	\(\chi_{3200}(67, \cdot)\)	n/a	30592	64
3200.2.df	\(\chi_{3200}(29, \cdot)\)	n/a	30592	64
3200.2.dh	\(\chi_{3200}(21, \cdot)\)	n/a	30592	64
3200.2.di	\(\chi_{3200}(3, \cdot)\)	n/a	30592	64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(640))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1600))\)\(^{\oplus 2}\)