Space of modular forms of level 64 and weight 16

• Label: 64.16
• Level: 64
• Weight: 16
• Dimension: 1069
• Nonzero newspaces: 4
• Sturm bound: 4096
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 64 = 2^{6} \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(4096\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(64))\).

	Total	New	Old
Modular forms	1956	1091	865
Cusp forms	1884	1069	815
Eisenstein series	72	22	50

Trace form

1069 * q - 8 * q^2 - 6 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 14348917 * q^9 - 8 * q^10 - 93786106 * q^11 - 8 * q^12 - 249054560 * q^13 - 8 * q^14 + 1366874996 * q^15 - 8 * q^16 - 2914219270 * q^17 - 8 * q^18 + 5208040914 * q^19 - 8 * q^20 - 5387796980 * q^21 - 64498267120 * q^22 - 8 * q^23 - 211994495008 * q^24 + 88400810201 * q^25 - 61505704048 * q^26 - 127470485568 * q^27 + 219776093952 * q^28 + 264813357992 * q^29 - 348327679128 * q^30 - 330151369328 * q^31 - 332318572768 * q^32 + 1203864895748 * q^33 + 1574362294992 * q^34 - 425575537444 * q^35 - 6804374861688 * q^36 - 645014447088 * q^37 + 5187890227952 * q^38 - 8 * q^39 - 7183373182368 * q^40 - 1386808528906 * q^41 + 15249634710032 * q^42 - 433351358818 * q^43 + 1659459904992 * q^44 - 5535722200284 * q^45 - 8 * q^46 + 10132462409256 * q^47 - 8 * q^48 - 1255640086471 * q^49 + 10085326880656 * q^50 + 40487440457908 * q^51 + 68835290191624 * q^52 + 30822993828400 * q^53 - 97072077723848 * q^54 + 73757548293688 * q^55 + 57525565626752 * q^56 - 39425416959200 * q^57 + 50478903531136 * q^58 + 172681442803694 * q^59 - 267417509893352 * q^60 - 32466979229408 * q^61 + 98091686054888 * q^62 - 412888309956484 * q^63 + 250148390516632 * q^64 - 55984661522616 * q^65 - 499436430190504 * q^66 + 633444884592690 * q^67 - 31156379591672 * q^68 - 216045869825444 * q^69 + 854610494252248 * q^70 - 278354148847048 * q^71 - 431283031456400 * q^72 + 334839221923830 * q^73 - 492777101473168 * q^74 - 1051061337453918 * q^75 + 1404376662325432 * q^76 - 36005177517364 * q^77 - 2700237825996176 * q^78 + 1360558258532056 * q^79 + 3350959944349856 * q^80 - 678210142882859 * q^81 - 2431832259285848 * q^82 - 396054094817286 * q^83 + 4023225569539112 * q^84 + 1035409163333008 * q^85 - 1041023913958608 * q^86 - 8 * q^87 - 3007957639468088 * q^88 - 840528633656506 * q^89 + 4666432533749992 * q^90 + 501384492577268 * q^91 + 6065951365842096 * q^92 + 2846296026002176 * q^93 - 4458227073999848 * q^94 - 3114419543807220 * q^95 - 7376260341716608 * q^96 + 1177015141282130 * q^97 + 7793338497178736 * q^98 + 373067189655986 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(64))\)

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
64.16.a	\(\chi_{64}(1, \cdot)\)	64.16.a.a	1	1
		64.16.a.b	1
		64.16.a.c	1
		64.16.a.d	1
		64.16.a.e	1
		64.16.a.f	1
		64.16.a.g	1
		64.16.a.h	1
		64.16.a.i	1
		64.16.a.j	1
		64.16.a.k	1
		64.16.a.l	2
		64.16.a.m	2
		64.16.a.n	2
		64.16.a.o	4
		64.16.a.p	4
		64.16.a.q	4
64.16.b	\(\chi_{64}(33, \cdot)\)	64.16.b.a	2	1
		64.16.b.b	8
		64.16.b.c	20
64.16.e	\(\chi_{64}(17, \cdot)\)	64.16.e.a	58	2
64.16.g	\(\chi_{64}(9, \cdot)\)	None	0	4
64.16.i	\(\chi_{64}(5, \cdot)\)	n/a	952	8

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

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces

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