Space of modular forms of level 128 and weight 2

• Label: 128.2
• Level: 128
• Weight: 2
• Dimension: 264
• Nonzero newspaces: 5
• Newform subspaces: 11
• Sturm bound: 2048
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 128 = 2^{7} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(2048\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(128))\).

	Total	New	Old
Modular forms	592	312	280
Cusp forms	433	264	169
Eisenstein series	159	48	111

Trace form

264 * 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 - 28 * q^21 - 16 * q^22 - 20 * q^23 - 16 * q^24 - 36 * q^25 - 16 * q^26 - 36 * q^27 - 16 * q^28 - 32 * q^29 - 16 * q^30 - 32 * q^31 - 16 * q^32 - 64 * q^33 - 16 * q^34 - 36 * q^35 - 16 * q^36 - 32 * q^37 - 16 * q^38 - 36 * q^39 - 16 * q^40 - 36 * q^41 - 16 * q^42 - 20 * q^43 - 16 * q^44 - 12 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 + 4 * q^49 + 32 * q^50 - 8 * q^51 + 80 * q^52 + 16 * q^53 + 112 * q^54 + 20 * q^55 + 96 * q^56 + 44 * q^57 + 128 * q^58 + 20 * q^59 + 176 * q^60 + 48 * q^61 + 80 * q^62 + 48 * q^63 + 176 * q^64 + 48 * q^65 + 176 * q^66 + 28 * q^67 + 80 * q^68 + 36 * q^69 + 176 * q^70 + 20 * q^71 + 128 * q^72 + 44 * q^73 + 96 * q^74 + 112 * q^76 - 12 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 20 * q^81 - 16 * q^82 - 52 * q^83 - 16 * q^84 - 8 * q^85 - 16 * q^86 - 68 * q^87 - 16 * q^88 - 84 * q^89 - 16 * q^90 - 60 * q^91 - 16 * q^92 - 64 * q^93 - 16 * q^94 - 72 * q^95 - 16 * q^96 - 96 * q^97 - 16 * q^98 - 64 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)

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
128.2.a	\(\chi_{128}(1, \cdot)\)	128.2.a.a	1	1
		128.2.a.b	1
		128.2.a.c	1
		128.2.a.d	1
128.2.b	\(\chi_{128}(65, \cdot)\)	128.2.b.a	2	1
		128.2.b.b	2
128.2.e	\(\chi_{128}(33, \cdot)\)	128.2.e.a	2	2
		128.2.e.b	2
128.2.g	\(\chi_{128}(17, \cdot)\)	128.2.g.a	4	4
		128.2.g.b	8
128.2.i	\(\chi_{128}(9, \cdot)\)	None	0	8
128.2.k	\(\chi_{128}(5, \cdot)\)	128.2.k.a	240	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces

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