Space of modular forms of level 128 and weight 4

• Label: 128.4
• Level: 128
• Weight: 4
• Dimension: 840
• Nonzero newspaces: 5
• Newform subspaces: 17
• Sturm bound: 4096
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 128 = 2^{7} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(4096\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(128))\).

	Total	New	Old
Modular forms	1616	888	728
Cusp forms	1456	840	616
Eisenstein series	160	48	112

Trace form

840 * 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 - 124 * q^21 - 16 * q^22 - 340 * q^23 - 16 * q^24 - 196 * q^25 - 16 * q^26 + 252 * q^27 - 16 * q^28 + 384 * q^29 - 16 * q^30 + 736 * q^31 - 16 * q^32 + 896 * q^33 - 16 * q^34 + 444 * q^35 - 16 * q^36 - 16 * q^38 - 612 * q^39 - 16 * q^40 - 964 * q^41 - 16 * q^42 - 820 * q^43 - 16 * q^44 - 300 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 + 1348 * q^49 + 5696 * q^50 + 1368 * q^51 + 6608 * q^52 + 1488 * q^53 + 3440 * q^54 + 276 * q^55 - 800 * q^56 - 1364 * q^57 - 4768 * q^58 - 1388 * q^59 - 9808 * q^60 - 3664 * q^61 - 5872 * q^62 - 2512 * q^63 - 12112 * q^64 - 3920 * q^65 - 10960 * q^66 - 2052 * q^67 - 4144 * q^68 - 2236 * q^69 - 4048 * q^70 - 236 * q^71 + 1280 * q^72 + 1708 * q^73 + 5248 * q^74 + 1696 * q^75 + 11888 * q^76 + 2420 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 788 * q^81 - 16 * q^82 - 2452 * q^83 - 16 * q^84 + 504 * q^85 - 16 * q^86 + 1276 * q^87 - 16 * q^88 + 3372 * q^89 - 16 * q^90 + 3588 * q^91 - 16 * q^92 + 4256 * q^93 - 16 * q^94 + 6072 * q^95 - 16 * q^96 + 5920 * q^97 - 16 * q^98 + 5408 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(128))\)

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
128.4.a	\(\chi_{128}(1, \cdot)\)	128.4.a.a	1	1
		128.4.a.b	1
		128.4.a.c	1
		128.4.a.d	1
		128.4.a.e	2
		128.4.a.f	2
		128.4.a.g	2
		128.4.a.h	2
128.4.b	\(\chi_{128}(65, \cdot)\)	128.4.b.a	2	1
		128.4.b.b	2
		128.4.b.c	2
		128.4.b.d	2
		128.4.b.e	4
128.4.e	\(\chi_{128}(33, \cdot)\)	128.4.e.a	10	2
		128.4.e.b	10
128.4.g	\(\chi_{128}(17, \cdot)\)	128.4.g.a	44	4
128.4.i	\(\chi_{128}(9, \cdot)\)	None	0	8
128.4.k	\(\chi_{128}(5, \cdot)\)	128.4.k.a	752	16

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces

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