Space of modular forms of level 1024 and weight 2

• Label: 1024.2
• Level: 1024
• Weight: 2
• Dimension: 18192
• Nonzero newspaces: 8
• Sturm bound: 131072
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 1024 = 2^{10} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(131072\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1024))\).

	Total	New	Old
Modular forms	33600	18672	14928
Cusp forms	31937	18192	13745
Eisenstein series	1663	480	1183

Trace form

18192 * q - 128 * q^2 - 96 * q^3 - 128 * q^4 - 128 * q^5 - 128 * q^6 - 96 * q^7 - 128 * q^8 - 160 * q^9 - 128 * q^10 - 96 * q^11 - 128 * q^12 - 128 * q^13 - 128 * q^14 - 96 * q^15 - 128 * q^16 - 192 * q^17 - 128 * q^18 - 96 * q^19 - 128 * q^20 - 128 * q^21 - 128 * q^22 - 96 * q^23 - 128 * q^24 - 160 * q^25 - 128 * q^26 - 96 * q^27 - 128 * q^28 - 128 * q^29 - 128 * q^30 - 96 * q^31 - 128 * q^32 - 224 * q^33 - 128 * q^34 - 96 * q^35 - 128 * q^36 - 128 * q^37 - 128 * q^38 - 96 * q^39 - 128 * q^40 - 160 * q^41 - 128 * q^42 - 96 * q^43 - 128 * q^44 - 128 * q^45 - 128 * q^46 - 96 * q^47 - 128 * q^48 - 192 * q^49 - 128 * q^50 - 96 * q^51 - 128 * q^52 - 128 * q^53 - 128 * q^54 - 96 * q^55 - 128 * q^56 - 160 * q^57 - 128 * q^58 - 96 * q^59 - 128 * q^60 - 128 * q^61 - 128 * q^62 - 96 * q^63 - 128 * q^64 - 256 * q^65 - 128 * q^66 - 96 * q^67 - 128 * q^68 - 128 * q^69 - 128 * q^70 - 96 * q^71 - 128 * q^72 - 160 * q^73 - 128 * q^74 - 96 * q^75 - 128 * q^76 - 128 * q^77 - 128 * q^78 - 96 * q^79 - 128 * q^80 - 192 * q^81 - 128 * q^82 - 96 * q^83 - 128 * q^84 - 128 * q^85 - 128 * q^86 - 96 * q^87 - 128 * q^88 - 160 * q^89 - 128 * q^90 - 96 * q^91 - 128 * q^92 - 128 * q^93 - 128 * q^94 - 96 * q^95 - 128 * q^96 - 224 * q^97 - 128 * q^98 - 96 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1024))\)

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
1024.2.a	\(\chi_{1024}(1, \cdot)\)	1024.2.a.a	2	1
		1024.2.a.b	2
		1024.2.a.c	2
		1024.2.a.d	2
		1024.2.a.e	2
		1024.2.a.f	2
		1024.2.a.g	4
		1024.2.a.h	4
		1024.2.a.i	4
		1024.2.a.j	4
1024.2.b	\(\chi_{1024}(513, \cdot)\)	1024.2.b.a	2	1
		1024.2.b.b	2
		1024.2.b.c	2
		1024.2.b.d	2
		1024.2.b.e	2
		1024.2.b.f	2
		1024.2.b.g	8
		1024.2.b.h	8
1024.2.e	\(\chi_{1024}(257, \cdot)\)	1024.2.e.a	2	2
		1024.2.e.b	2
		1024.2.e.c	2
		1024.2.e.d	2
		1024.2.e.e	2
		1024.2.e.f	2
		1024.2.e.g	4
		1024.2.e.h	4
		1024.2.e.i	4
		1024.2.e.j	4
		1024.2.e.k	4
		1024.2.e.l	4
		1024.2.e.m	4
		1024.2.e.n	4
		1024.2.e.o	4
		1024.2.e.p	8
1024.2.g	\(\chi_{1024}(129, \cdot)\)	1024.2.g.a	16	4
		1024.2.g.b	16
		1024.2.g.c	16
		1024.2.g.d	16
		1024.2.g.e	16
		1024.2.g.f	16
		1024.2.g.g	16
		1024.2.g.h	16
1024.2.i	\(\chi_{1024}(65, \cdot)\)	n/a	224	8
1024.2.k	\(\chi_{1024}(33, \cdot)\)	n/a	480	16
1024.2.m	\(\chi_{1024}(17, \cdot)\)	n/a	992	32
1024.2.o	\(\chi_{1024}(9, \cdot)\)	None	0	64
1024.2.q	\(\chi_{1024}(5, \cdot)\)	n/a	16256	128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 11}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1024))\)\(^{\oplus 1}\)