Space of modular forms of level 128 and weight 5

• Label: 128.5
• Level: 128
• Weight: 5
• Dimension: 1128
• Nonzero newspaces: 5
• Newform subspaces: 10
• Sturm bound: 5120
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 128 = 2^{7} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(5120\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(128))\).

	Total	New	Old
Modular forms	2128	1176	952
Cusp forms	1968	1128	840
Eisenstein series	160	48	112

Trace form

1128 * 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 - 8 * q^15 - 16 * q^16 - 24 * q^17 - 16 * q^18 - 12 * q^19 - 16 * q^20 + 308 * q^21 - 16 * q^22 + 1140 * q^23 - 16 * q^24 - 1364 * q^25 - 16 * q^26 - 3660 * q^27 - 16 * q^28 - 1744 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 + 3936 * q^33 - 16 * q^34 + 5172 * q^35 - 16 * q^36 + 3632 * q^37 - 16 * q^38 + 2676 * q^39 - 16 * q^40 - 2900 * q^41 - 16 * q^42 - 5580 * q^43 - 16 * q^44 - 3164 * q^45 - 16 * q^46 - 8 * q^47 - 16 * q^48 - 9628 * q^49 - 43072 * q^50 - 8400 * q^51 - 17968 * q^52 + 1904 * q^53 + 31088 * q^54 + 11764 * q^55 + 49376 * q^56 + 29932 * q^57 + 65504 * q^58 + 13044 * q^59 + 63920 * q^60 + 15088 * q^61 + 11792 * q^62 - 32 * q^63 - 24400 * q^64 - 16144 * q^65 - 70864 * q^66 - 18892 * q^67 - 53296 * q^68 - 38860 * q^69 - 122320 * q^70 - 19980 * q^71 - 81664 * q^72 - 29460 * q^73 - 33280 * q^74 + 184 * q^75 + 28272 * q^76 + 28404 * q^77 + 99344 * q^78 + 50168 * q^79 + 105248 * q^80 + 41452 * q^81 - 16 * q^82 - 10572 * q^83 - 16 * q^84 - 17416 * q^85 - 16 * q^86 - 49292 * q^87 - 16 * q^88 - 54548 * q^89 - 16 * q^90 - 31884 * q^91 - 16 * q^92 - 17488 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 + 24288 * q^97 - 16 * q^98 + 46904 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(128))\)

We only show spaces with odd 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
128.5.c	\(\chi_{128}(127, \cdot)\)	128.5.c.a	8	1
		128.5.c.b	8
128.5.d	\(\chi_{128}(63, \cdot)\)	128.5.d.a	2	1
		128.5.d.b	2
		128.5.d.c	4
		128.5.d.d	8
128.5.f	\(\chi_{128}(31, \cdot)\)	128.5.f.a	14	2
		128.5.f.b	14
128.5.h	\(\chi_{128}(15, \cdot)\)	128.5.h.a	60	4
128.5.j	\(\chi_{128}(7, \cdot)\)	None	0	8
128.5.l	\(\chi_{128}(3, \cdot)\)	128.5.l.a	1008	16

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces

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