Space of modular forms of level 512 and weight 2

• Label: 512.2
• Level: 512
• Weight: 2
• Dimension: 4496
• Nonzero newspaces: 7
• Newform subspaces: 34
• Sturm bound: 32768
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 512 = 2^{9} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 7 \)
Newform subspaces:			\( 34 \)
Sturm bound:			\(32768\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(512))\).

	Total	New	Old
Modular forms	8576	4720	3856
Cusp forms	7809	4496	3313
Eisenstein series	767	224	543

Trace form

4496 * q - 64 * q^2 - 48 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 48 * q^7 - 64 * q^8 - 80 * q^9 - 64 * q^10 - 48 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 48 * q^15 - 64 * q^16 - 96 * q^17 - 64 * q^18 - 48 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 48 * q^23 - 64 * q^24 - 80 * q^25 - 64 * q^26 - 48 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 48 * q^31 - 64 * q^32 - 112 * q^33 - 64 * q^34 - 48 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 48 * q^39 - 64 * q^40 - 80 * q^41 - 64 * q^42 - 48 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 48 * q^47 - 64 * q^48 - 96 * q^49 - 64 * q^50 - 48 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 48 * q^55 - 64 * q^56 - 80 * q^57 - 64 * q^58 - 48 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 128 * q^65 - 64 * q^66 - 48 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 48 * q^71 - 64 * q^72 - 80 * q^73 - 64 * q^74 - 48 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 48 * q^79 - 64 * q^80 - 96 * q^81 - 64 * q^82 - 48 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 48 * q^87 - 64 * q^88 - 80 * q^89 - 64 * q^90 - 48 * q^91 - 64 * q^92 - 112 * q^93 - 64 * q^94 - 48 * q^95 - 64 * q^96 - 112 * q^97 - 64 * q^98 - 48 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(512))\)

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
512.2.a	\(\chi_{512}(1, \cdot)\)	512.2.a.a	2	1
		512.2.a.b	2
		512.2.a.c	2
		512.2.a.d	2
		512.2.a.e	2
		512.2.a.f	2
		512.2.a.g	4
512.2.b	\(\chi_{512}(257, \cdot)\)	512.2.b.a	2	1
		512.2.b.b	2
		512.2.b.c	4
		512.2.b.d	4
		512.2.b.e	4
512.2.e	\(\chi_{512}(129, \cdot)\)	512.2.e.a	2	2
		512.2.e.b	2
		512.2.e.c	2
		512.2.e.d	2
		512.2.e.e	2
		512.2.e.f	2
		512.2.e.g	2
		512.2.e.h	2
		512.2.e.i	8
		512.2.e.j	8
512.2.g	\(\chi_{512}(65, \cdot)\)	512.2.g.a	4	4
		512.2.g.b	4
		512.2.g.c	4
		512.2.g.d	4
		512.2.g.e	8
		512.2.g.f	8
		512.2.g.g	8
		512.2.g.h	8
512.2.i	\(\chi_{512}(33, \cdot)\)	512.2.i.a	56	8
		512.2.i.b	56
512.2.k	\(\chi_{512}(17, \cdot)\)	512.2.k.a	240	16
512.2.m	\(\chi_{512}(9, \cdot)\)	None	0	32
512.2.o	\(\chi_{512}(5, \cdot)\)	512.2.o.a	4032	64

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(512))\) into lower level spaces

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