Space of modular forms of level 64 and weight 22

• Label: 64.22
• Level: 64
• Weight: 22
• Dimension: 1501
• Nonzero newspaces: 4
• Sturm bound: 5632
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 64 = 2^{6} \)
Weight:	\( k \)	=	\( 22 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(5632\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(64))\).

	Total	New	Old
Modular forms	2724	1523	1201
Cusp forms	2652	1501	1151
Eisenstein series	72	22	50

Trace form

1501 * q - 8 * q^2 - 6 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 10460353213 * q^9 - 8 * q^10 - 67333320746 * q^11 - 8 * q^12 - 1065395863664 * q^13 - 8 * q^14 - 4613203125004 * q^15 - 8 * q^16 - 6962857988022 * q^17 - 8 * q^18 + 46007763621426 * q^19 - 8 * q^20 + 132781988108764 * q^21 - 207411361090032 * q^22 - 8 * q^23 - 1945658207807008 * q^24 + 637048321772881 * q^25 - 1506625290169968 * q^26 - 1147760716556928 * q^27 + 11978218049315072 * q^28 - 4866346900433208 * q^29 - 16217339993829528 * q^30 + 9835539443769616 * q^31 - 12832721772527328 * q^32 - 42872757726145228 * q^33 + 58324591899126992 * q^34 + 19253478556034876 * q^35 - 296417618048471928 * q^36 - 25075936097793568 * q^37 + 303109027666885872 * q^38 - 8 * q^39 - 363206157537854368 * q^40 + 510309577544344566 * q^41 - 980887809273580528 * q^42 - 215332019803969394 * q^43 - 959490752542847008 * q^44 + 828356648574617748 * q^45 - 8 * q^46 - 1051982644716600984 * q^47 - 8 * q^48 + 1837350517946442953 * q^49 - 4761634387503570032 * q^50 - 6784243964339970860 * q^51 - 8655710943494332664 * q^52 + 4030944480231746368 * q^53 - 4994095300087806152 * q^54 + 15854219360527201336 * q^55 + 13445791338293702016 * q^56 + 2559856001679390352 * q^57 - 24235593818026622336 * q^58 + 21123007083356949214 * q^59 + 34373655846659160856 * q^60 + 2876746575441830032 * q^61 - 9454210277557709848 * q^62 + 96258845731845948860 * q^63 - 28235118983318354024 * q^64 + 2883914131812497576 * q^65 + 111234197313377019992 * q^66 + 85371272536705140882 * q^67 - 104659289810037971960 * q^68 - 39855976718185394420 * q^69 + 279305961159540045016 * q^70 - 135249633480998712264 * q^71 - 215147916304966389392 * q^72 + 48694326242424071158 * q^73 + 149453752937774472816 * q^74 - 612779223988624340910 * q^75 - 235541415539266676552 * q^76 + 132554470675161717596 * q^77 + 226776658842727689328 * q^78 - 234613589151699565416 * q^79 - 860612604870301954912 * q^80 + 994446341328046922677 * q^81 - 708517628372968195928 * q^82 - 317463236552669319686 * q^83 + 1424936216815736264744 * q^84 + 257778402032356066528 * q^85 - 917406725370159511248 * q^86 - 8 * q^87 - 418946962671126792248 * q^88 + 1439609648740966873318 * q^89 + 4037191479561093749992 * q^90 - 144326756239046079756 * q^91 - 6603731275935646802256 * q^92 - 2037517980701178374048 * q^93 + 2424473717652338934808 * q^94 + 1411330138695550130700 * q^95 + 4329988420061566228352 * q^96 - 2359410602208113631422 * q^97 - 11226390629590293575056 * q^98 - 2710306841442932184622 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.22.a	\(\chi_{64}(1, \cdot)\)	64.22.a.a	1	1
		64.22.a.b	1
		64.22.a.c	1
		64.22.a.d	1
		64.22.a.e	1
		64.22.a.f	1
		64.22.a.g	1
		64.22.a.h	2
		64.22.a.i	2
		64.22.a.j	2
		64.22.a.k	2
		64.22.a.l	3
		64.22.a.m	3
		64.22.a.n	4
		64.22.a.o	5
		64.22.a.p	5
		64.22.a.q	6
64.22.b	\(\chi_{64}(33, \cdot)\)	64.22.b.a	2	1
		64.22.b.b	12
		64.22.b.c	28
64.22.e	\(\chi_{64}(17, \cdot)\)	64.22.e.a	82	2
64.22.g	\(\chi_{64}(9, \cdot)\)	None	0	4
64.22.i	\(\chi_{64}(5, \cdot)\)	n/a	1336	8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)