Space of modular forms of level 128 and weight 8

• Label: 128.8
• Level: 128
• Weight: 8
• Dimension: 1992
• Nonzero newspaces: 5
• Sturm bound: 8192
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 128 = 2^{7} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 5 \)
Sturm bound:			\(8192\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(128))\).

	Total	New	Old
Modular forms	3664	2040	1624
Cusp forms	3504	1992	1512
Eisenstein series	160	48	112

Trace form

1992 * q - 16 * q^2 - 12 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 12 * q^7 - 16 * q^8 - 20 * q^9 - 16 * q^10 - 12 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 24 * q^17 - 16 * q^18 - 12 * q^19 - 16 * q^20 - 8764 * q^21 - 16 * q^22 + 143404 * q^23 - 16 * q^24 - 64516 * q^25 - 16 * q^26 - 476100 * q^27 - 16 * q^28 + 103360 * q^29 - 16 * q^30 + 714976 * q^31 - 16 * q^32 + 396032 * q^33 - 16 * q^34 - 816516 * q^35 - 16 * q^36 - 831168 * q^37 - 16 * q^38 + 283932 * q^39 - 16 * q^40 + 1765116 * q^41 - 16 * q^42 - 366196 * q^43 - 16 * q^44 - 295020 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 + 3294148 * q^49 + 4634816 * q^50 - 3002088 * q^51 - 20409904 * q^52 - 3631280 * q^53 + 2519408 * q^54 + 4190996 * q^55 + 21474528 * q^56 + 12408748 * q^57 + 20716256 * q^58 + 1835924 * q^59 - 8672848 * q^60 - 9119568 * q^61 - 20695024 * q^62 - 10001872 * q^63 - 45674320 * q^64 - 11415120 * q^65 - 15028432 * q^66 + 1940668 * q^67 + 17500112 * q^68 + 19153028 * q^69 + 71980592 * q^70 + 12348692 * q^71 + 45454592 * q^72 + 10136492 * q^73 - 8428800 * q^74 - 11573024 * q^75 - 77885840 * q^76 - 27123084 * q^77 - 58970608 * q^78 - 16 * q^79 + 63108896 * q^80 + 46160620 * q^81 - 16 * q^82 + 9565868 * q^83 - 16 * q^84 - 14443016 * q^85 - 16 * q^86 - 40789124 * q^87 - 16 * q^88 - 30457812 * q^89 - 16 * q^90 + 3406980 * q^91 - 16 * q^92 + 28999520 * q^93 - 16 * q^94 + 54871992 * q^95 - 16 * q^96 + 44451360 * q^97 - 16 * q^98 + 9738464 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(128))\)

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
128.8.a	\(\chi_{128}(1, \cdot)\)	128.8.a.a	3	1
		128.8.a.b	3
		128.8.a.c	3
		128.8.a.d	3
		128.8.a.e	4
		128.8.a.f	4
		128.8.a.g	4
		128.8.a.h	4
128.8.b	\(\chi_{128}(65, \cdot)\)	128.8.b.a	2	1
		128.8.b.b	2
		128.8.b.c	4
		128.8.b.d	4
		128.8.b.e	4
		128.8.b.f	4
		128.8.b.g	8
128.8.e	\(\chi_{128}(33, \cdot)\)	128.8.e.a	26	2
		128.8.e.b	26
128.8.g	\(\chi_{128}(17, \cdot)\)	n/a	108	4
128.8.i	\(\chi_{128}(9, \cdot)\)	None	0	8
128.8.k	\(\chi_{128}(5, \cdot)\)	n/a	1776	16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces

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