Space of modular forms of level 64 and weight 7

• Label: 64.7
• Level: 64
• Weight: 7
• Dimension: 421
• Nonzero newspaces: 4
• Newform subspaces: 9
• Sturm bound: 1792
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 64 = 2^{6} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1792\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(64))\).

	Total	New	Old
Modular forms	804	443	361
Cusp forms	732	421	311
Eisenstein series	72	22	50

Trace form

421 * q - 8 * q^2 - 6 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 719 * q^9 - 8 * q^10 - 1366 * q^11 - 8 * q^12 + 5032 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 9790 * q^17 - 8 * q^18 - 3942 * q^19 - 8 * q^20 + 16516 * q^21 - 63728 * q^22 + 13116 * q^23 + 160992 * q^24 + 25549 * q^25 - 10608 * q^26 - 35784 * q^27 - 171008 * q^28 - 66408 * q^29 - 206488 * q^30 - 16 * q^31 + 117792 * q^32 + 177772 * q^33 + 278992 * q^34 + 112412 * q^35 + 365192 * q^36 - 48248 * q^37 - 200208 * q^38 - 254404 * q^39 - 575648 * q^40 - 175370 * q^41 - 173808 * q^42 + 267978 * q^43 + 480992 * q^44 + 320300 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 323583 * q^49 + 705424 * q^50 + 19612 * q^51 - 1275128 * q^52 - 301112 * q^53 - 1259720 * q^54 + 698108 * q^55 + 326528 * q^56 + 217768 * q^57 + 1770112 * q^58 - 1811446 * q^59 + 2511640 * q^60 - 196568 * q^61 + 541160 * q^62 - 1155176 * q^64 + 356232 * q^65 - 3102120 * q^66 + 3141978 * q^67 - 1847288 * q^68 - 799004 * q^69 - 2272040 * q^70 + 801020 * q^71 + 787312 * q^72 + 135926 * q^73 + 2924144 * q^74 - 4017082 * q^75 + 4565176 * q^76 + 324804 * q^77 - 3782288 * q^78 + 1721848 * q^79 - 2090336 * q^80 + 1776533 * q^81 + 6966952 * q^82 + 288314 * q^83 + 5971496 * q^84 - 801272 * q^85 - 828368 * q^86 - 2029892 * q^87 - 4695608 * q^88 - 4407402 * q^89 - 11466008 * q^90 - 302404 * q^91 - 10105424 * q^92 + 2013904 * q^93 - 2508776 * q^94 - 16 * q^95 + 3708032 * q^96 + 231018 * q^97 + 10348912 * q^98 + 277346 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.7.c	\(\chi_{64}(63, \cdot)\)	64.7.c.a	1	1
		64.7.c.b	2
		64.7.c.c	2
		64.7.c.d	2
		64.7.c.e	4
64.7.d	\(\chi_{64}(31, \cdot)\)	64.7.d.a	4	1
		64.7.d.b	8
64.7.f	\(\chi_{64}(15, \cdot)\)	64.7.f.a	22	2
64.7.h	\(\chi_{64}(7, \cdot)\)	None	0	4
64.7.j	\(\chi_{64}(3, \cdot)\)	64.7.j.a	376	8

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

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