Space of modular forms of level 64 and weight 8

• Label: 64.8
• Level: 64
• Weight: 8
• Dimension: 493
• Nonzero newspaces: 4
• Newform subspaces: 15
• Sturm bound: 2048
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 64 = 2^{6} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 15 \)
Sturm bound:			\(2048\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(64))\).

	Total	New	Old
Modular forms	932	515	417
Cusp forms	860	493	367
Eisenstein series	72	22	50

Trace form

493 * q - 8 * q^2 - 6 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 2197 * q^9 - 8 * q^10 - 1210 * q^11 - 8 * q^12 - 7072 * q^13 - 8 * q^14 + 26996 * q^15 - 8 * q^16 - 5830 * q^17 - 8 * q^18 - 60590 * q^19 - 8 * q^20 + 36172 * q^21 + 274448 * q^22 - 8 * q^23 - 598048 * q^24 - 13639 * q^25 + 727952 * q^26 + 233664 * q^27 + 390912 * q^28 - 103384 * q^29 - 1739928 * q^30 - 357488 * q^31 - 1071328 * q^32 - 400444 * q^33 + 403152 * q^34 + 251996 * q^35 + 4069512 * q^36 + 1465168 * q^37 + 1244912 * q^38 - 8 * q^39 - 2686368 * q^40 - 2967562 * q^41 - 3858928 * q^42 - 569762 * q^43 + 3370464 * q^44 + 1417956 * q^45 - 8 * q^46 + 2076456 * q^47 - 8 * q^48 + 1845625 * q^49 - 2317424 * q^50 - 8596172 * q^51 + 10204936 * q^52 - 3866000 * q^53 - 1259720 * q^54 + 8382008 * q^55 - 10737280 * q^56 + 4470496 * q^57 - 10358144 * q^58 + 8537006 * q^59 + 4336408 * q^60 + 307424 * q^61 + 10348520 * q^62 - 28298884 * q^63 + 22837144 * q^64 - 916536 * q^65 + 7515224 * q^66 + 9445810 * q^67 - 8750072 * q^68 - 1865444 * q^69 - 35990312 * q^70 + 24697400 * q^71 - 22727312 * q^72 - 2836490 * q^73 + 4214384 * q^74 - 28733598 * q^75 + 38942904 * q^76 + 10982156 * q^77 + 68832880 * q^78 + 9075160 * q^79 - 78362464 * q^80 - 10077611 * q^81 - 49314648 * q^82 - 4531206 * q^83 + 17056808 * q^84 + 4452048 * q^85 + 69535536 * q^86 - 8 * q^87 + 52517832 * q^88 + 20895686 * q^89 + 31733992 * q^90 - 2587660 * q^91 - 54440784 * q^92 - 15434624 * q^93 - 74691560 * q^94 + 4900620 * q^95 - 112868992 * q^96 - 33071086 * q^97 - 62769040 * q^98 - 18797518 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.8.a	\(\chi_{64}(1, \cdot)\)	64.8.a.a	1	1
		64.8.a.b	1
		64.8.a.c	1
		64.8.a.d	1
		64.8.a.e	1
		64.8.a.f	1
		64.8.a.g	1
		64.8.a.h	2
		64.8.a.i	2
		64.8.a.j	2
64.8.b	\(\chi_{64}(33, \cdot)\)	64.8.b.a	2	1
		64.8.b.b	4
		64.8.b.c	8
64.8.e	\(\chi_{64}(17, \cdot)\)	64.8.e.a	26	2
64.8.g	\(\chi_{64}(9, \cdot)\)	None	0	4
64.8.i	\(\chi_{64}(5, \cdot)\)	64.8.i.a	440	8

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

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