Space of modular forms of level 64 and weight 10

• Label: 64.10
• Level: 64
• Weight: 10
• Dimension: 637
• Nonzero newspaces: 4
• Newform subspaces: 18
• Sturm bound: 2560
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 64 = 2^{6} \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(2560\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(64))\).

	Total	New	Old
Modular forms	1188	659	529
Cusp forms	1116	637	479
Eisenstein series	72	22	50

Trace form

637 * q - 8 * q^2 - 6 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 19693 * q^9 - 8 * q^10 - 65866 * q^11 - 8 * q^12 + 194608 * q^13 - 8 * q^14 - 405004 * q^15 - 8 * q^16 + 407978 * q^17 - 8 * q^18 + 480882 * q^19 - 8 * q^20 - 1959236 * q^21 + 3576336 * q^22 - 8 * q^23 + 12096992 * q^24 + 4933921 * q^25 - 2105968 * q^26 - 6364416 * q^27 - 21791488 * q^28 - 1266808 * q^29 + 44263272 * q^30 + 11082256 * q^31 + 29441312 * q^32 - 190636 * q^33 - 38537008 * q^34 - 23026564 * q^35 - 110500728 * q^36 + 17001152 * q^37 + 66947312 * q^38 - 8 * q^39 + 97089632 * q^40 + 1161206 * q^41 - 224559088 * q^42 + 34881070 * q^43 + 146176992 * q^44 - 14308812 * q^45 - 8 * q^46 - 97593624 * q^47 - 8 * q^48 + 14539433 * q^49 + 182758288 * q^50 - 332675180 * q^51 - 25227512 * q^52 + 161472928 * q^53 - 646232264 * q^54 + 280217656 * q^55 + 203163008 * q^56 - 377672144 * q^57 + 855153280 * q^58 - 670653826 * q^59 + 230939416 * q^60 + 209365552 * q^61 - 597609496 * q^62 + 1413881660 * q^63 - 1364809832 * q^64 + 409307496 * q^65 + 186013784 * q^66 - 1413262638 * q^67 + 1004327944 * q^68 - 607316180 * q^69 + 1869092056 * q^70 - 476202952 * q^71 - 714729104 * q^72 + 927119350 * q^73 - 2182183312 * q^74 + 3347963250 * q^75 - 888710984 * q^76 - 277316164 * q^77 + 5243787376 * q^78 - 4182694632 * q^79 - 5193915232 * q^80 - 721500299 * q^81 + 3136405672 * q^82 + 1637053434 * q^83 + 6148771880 * q^84 + 2166685888 * q^85 - 988828368 * q^86 - 8 * q^87 - 4940685368 * q^88 - 4491535450 * q^89 - 7222410008 * q^90 - 2019528204 * q^91 + 1729489584 * q^92 + 1068636832 * q^93 + 6710490136 * q^94 + 5087413260 * q^95 + 10366581632 * q^96 + 3131588962 * q^97 + 2543861360 * q^98 - 3713593966 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.10.a	\(\chi_{64}(1, \cdot)\)	64.10.a.a	1	1
		64.10.a.b	1
		64.10.a.c	1
		64.10.a.d	1
		64.10.a.e	1
		64.10.a.f	1
		64.10.a.g	1
		64.10.a.h	1
		64.10.a.i	1
		64.10.a.j	2
		64.10.a.k	2
		64.10.a.l	2
		64.10.a.m	2
64.10.b	\(\chi_{64}(33, \cdot)\)	64.10.b.a	2	1
		64.10.b.b	4
		64.10.b.c	12
64.10.e	\(\chi_{64}(17, \cdot)\)	64.10.e.a	34	2
64.10.g	\(\chi_{64}(9, \cdot)\)	None	0	4
64.10.i	\(\chi_{64}(5, \cdot)\)	64.10.i.a	568	8

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)