Space of modular forms of level 1664 and weight 2

• Label: 1664.2
• Level: 1664
• Weight: 2
• Dimension: 47280
• Nonzero newspaces: 36
• Sturm bound: 344064
• Trace bound: 26

Defining parameters

Level:	\( N \)	=	\( 1664 = 2^{7} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(344064\)
Trace bound:			\(26\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1664))\).

	Total	New	Old
Modular forms	87936	48336	39600
Cusp forms	84097	47280	36817
Eisenstein series	3839	1056	2783

Trace form

47280 * q - 160 * q^2 - 120 * q^3 - 160 * q^4 - 160 * q^5 - 160 * q^6 - 120 * q^7 - 160 * q^8 - 200 * q^9 - 160 * q^10 - 120 * q^11 - 160 * q^12 - 176 * q^13 - 352 * q^14 - 112 * q^15 - 160 * q^16 - 240 * q^17 - 160 * q^18 - 120 * q^19 - 160 * q^20 - 136 * q^21 - 160 * q^22 - 104 * q^23 - 160 * q^24 - 168 * q^25 - 176 * q^26 - 216 * q^27 - 160 * q^28 - 128 * q^29 - 160 * q^30 - 80 * q^31 - 160 * q^32 - 256 * q^33 - 160 * q^34 - 72 * q^35 - 160 * q^36 - 128 * q^37 - 160 * q^38 - 108 * q^39 - 352 * q^40 - 168 * q^41 - 160 * q^42 - 104 * q^43 - 160 * q^44 - 168 * q^45 - 160 * q^46 - 112 * q^47 - 160 * q^48 - 296 * q^49 - 256 * q^50 - 128 * q^51 - 272 * q^52 - 416 * q^53 - 416 * q^54 - 184 * q^55 - 384 * q^56 - 328 * q^57 - 448 * q^58 - 184 * q^59 - 544 * q^60 - 288 * q^61 - 352 * q^62 - 240 * q^63 - 544 * q^64 - 240 * q^65 - 736 * q^66 - 200 * q^67 - 352 * q^68 - 264 * q^69 - 544 * q^70 - 184 * q^71 - 448 * q^72 - 328 * q^73 - 384 * q^74 - 144 * q^75 - 416 * q^76 - 168 * q^77 - 272 * q^78 - 256 * q^79 - 256 * q^80 - 248 * q^81 - 160 * q^82 - 40 * q^83 - 160 * q^84 - 176 * q^85 - 160 * q^86 - 8 * q^87 - 160 * q^88 - 72 * q^89 - 160 * q^90 - 84 * q^91 - 352 * q^92 - 64 * q^93 - 160 * q^94 - 160 * q^96 - 192 * q^97 - 160 * q^98 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1664))\)

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
1664.2.a	\(\chi_{1664}(1, \cdot)\)	1664.2.a.a	1	1
		1664.2.a.b	1
		1664.2.a.c	1
		1664.2.a.d	1
		1664.2.a.e	1
		1664.2.a.f	1
		1664.2.a.g	1
		1664.2.a.h	1
		1664.2.a.i	1
		1664.2.a.j	1
		1664.2.a.k	1
		1664.2.a.l	1
		1664.2.a.m	1
		1664.2.a.n	1
		1664.2.a.o	1
		1664.2.a.p	1
		1664.2.a.q	1
		1664.2.a.r	1
		1664.2.a.s	1
		1664.2.a.t	1
		1664.2.a.u	2
		1664.2.a.v	2
		1664.2.a.w	2
		1664.2.a.x	2
		1664.2.a.y	5
		1664.2.a.z	5
		1664.2.a.ba	5
		1664.2.a.bb	5
1664.2.b	\(\chi_{1664}(833, \cdot)\)	1664.2.b.a	2	1
		1664.2.b.b	2
		1664.2.b.c	2
		1664.2.b.d	2
		1664.2.b.e	4
		1664.2.b.f	4
		1664.2.b.g	4
		1664.2.b.h	4
		1664.2.b.i	4
		1664.2.b.j	8
		1664.2.b.k	12
1664.2.e	\(\chi_{1664}(961, \cdot)\)	1664.2.e.a	2	1
		1664.2.e.b	2
		1664.2.e.c	4
		1664.2.e.d	4
		1664.2.e.e	8
		1664.2.e.f	12
		1664.2.e.g	12
		1664.2.e.h	12
1664.2.f	\(\chi_{1664}(129, \cdot)\)	1664.2.f.a	14	1
		1664.2.f.b	14
		1664.2.f.c	14
		1664.2.f.d	14
1664.2.i	\(\chi_{1664}(1153, \cdot)\)	n/a	112	2
1664.2.k	\(\chi_{1664}(255, \cdot)\)	n/a	112	2
1664.2.l	\(\chi_{1664}(671, \cdot)\)	n/a	104	2
1664.2.n	\(\chi_{1664}(417, \cdot)\)	1664.2.n.a	48	2
		1664.2.n.b	48
1664.2.p	\(\chi_{1664}(545, \cdot)\)	n/a	104	2
1664.2.s	\(\chi_{1664}(31, \cdot)\)	n/a	104	2
1664.2.u	\(\chi_{1664}(447, \cdot)\)	n/a	112	2
1664.2.w	\(\chi_{1664}(257, \cdot)\)	n/a	112	2
1664.2.z	\(\chi_{1664}(321, \cdot)\)	n/a	112	2
1664.2.ba	\(\chi_{1664}(1089, \cdot)\)	n/a	112	2
1664.2.bd	\(\chi_{1664}(239, \cdot)\)	n/a	216	4
1664.2.bf	\(\chi_{1664}(209, \cdot)\)	n/a	192	4
1664.2.bg	\(\chi_{1664}(337, \cdot)\)	n/a	216	4
1664.2.bi	\(\chi_{1664}(47, \cdot)\)	n/a	216	4
1664.2.bk	\(\chi_{1664}(63, \cdot)\)	n/a	224	4
1664.2.bn	\(\chi_{1664}(223, \cdot)\)	n/a	208	4
1664.2.bp	\(\chi_{1664}(225, \cdot)\)	n/a	208	4
1664.2.br	\(\chi_{1664}(289, \cdot)\)	n/a	208	4
1664.2.bs	\(\chi_{1664}(479, \cdot)\)	n/a	208	4
1664.2.bu	\(\chi_{1664}(383, \cdot)\)	n/a	224	4
1664.2.bw	\(\chi_{1664}(135, \cdot)\)	None	0	8
1664.2.by	\(\chi_{1664}(105, \cdot)\)	None	0	8
1664.2.cb	\(\chi_{1664}(25, \cdot)\)	None	0	8
1664.2.cc	\(\chi_{1664}(343, \cdot)\)	None	0	8
1664.2.cf	\(\chi_{1664}(15, \cdot)\)	n/a	432	8
1664.2.ch	\(\chi_{1664}(17, \cdot)\)	n/a	432	8
1664.2.ci	\(\chi_{1664}(81, \cdot)\)	n/a	432	8
1664.2.ck	\(\chi_{1664}(175, \cdot)\)	n/a	432	8
1664.2.cn	\(\chi_{1664}(99, \cdot)\)	n/a	3552	16
1664.2.cp	\(\chi_{1664}(53, \cdot)\)	n/a	3072	16
1664.2.cr	\(\chi_{1664}(77, \cdot)\)	n/a	3552	16
1664.2.cs	\(\chi_{1664}(83, \cdot)\)	n/a	3552	16
1664.2.cv	\(\chi_{1664}(7, \cdot)\)	None	0	16
1664.2.cx	\(\chi_{1664}(9, \cdot)\)	None	0	16
1664.2.cy	\(\chi_{1664}(121, \cdot)\)	None	0	16
1664.2.db	\(\chi_{1664}(71, \cdot)\)	None	0	16
1664.2.dc	\(\chi_{1664}(115, \cdot)\)	n/a	7104	32
1664.2.de	\(\chi_{1664}(69, \cdot)\)	n/a	7104	32
1664.2.dg	\(\chi_{1664}(29, \cdot)\)	n/a	7104	32
1664.2.dj	\(\chi_{1664}(11, \cdot)\)	n/a	7104	32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1664)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(832))\)\(^{\oplus 2}\)