Space of modular forms of level 8 and weight 21

• Label: 8.21
• Level: 8
• Weight: 21
• Dimension: 19
• Nonzero newspaces: 1
• Newform subspaces: 2
• Sturm bound: 84
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 8 = 2^{3} \)
Weight:	\( k \)	=	\( 21 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(\Gamma_1(8))\).

	Total	New	Old
Modular forms	43	21	22
Cusp forms	37	19	18
Eisenstein series	6	2	4

Trace form

19 * q + 626 * q^2 - 2 * q^3 + 1773556 * q^4 + 25323676 * q^6 - 2031549544 * q^8 + 19758444937 * q^9 + 742754160 * q^10 - 14520628706 * q^11 - 92518091912 * q^12 - 431248136928 * q^14 + 140976757264 * q^16 + 990389375398 * q^17 + 5272759222774 * q^18 - 1375336086082 * q^19 - 32520172742880 * q^20 - 109675699217572 * q^22 + 144938556063376 * q^24 - 300360045368285 * q^25 + 154289718058128 * q^26 - 514588541331140 * q^27 - 394619539621440 * q^28 + 223250517248160 * q^30 - 1707914682142624 * q^32 - 379273727638900 * q^33 - 4373483391631324 * q^34 + 3615863153468160 * q^35 + 11585741011529500 * q^36 + 11866377694661788 * q^38 + 11813880412973760 * q^40 - 8427241614192506 * q^41 + 38127588900300480 * q^42 - 24717352370364898 * q^43 - 11262977142561032 * q^44 - 21739818881100192 * q^46 + 153956946591726688 * q^48 - 173173121721250637 * q^49 + 139361869584456530 * q^50 - 417243550710750724 * q^51 - 44583718369992480 * q^52 + 131060624290419256 * q^54 - 505574909383001472 * q^56 - 638353406270838580 * q^57 - 677523738697093680 * q^58 - 80800002484130978 * q^59 + 1631640690429240000 * q^60 + 1780090172849178240 * q^62 + 1328363317618417216 * q^64 + 1575343920200472960 * q^65 + 3043614561170466056 * q^66 - 1808783156240800642 * q^67 - 2362666796221870232 * q^68 - 6151558949299572480 * q^70 + 4959295908955144264 * q^72 + 3866104143546483398 * q^73 - 5642095430673385488 * q^74 + 24308156015351409310 * q^75 - 9480723535297927816 * q^76 - 14599907290310144160 * q^78 - 22104885212702947200 * q^80 + 13599596957313525631 * q^81 - 15707154812006670172 * q^82 - 77448386448570160322 * q^83 + 17095266896298568320 * q^84 + 36403346004507897820 * q^86 - 13164074256796170352 * q^88 + 33127276190960144518 * q^89 - 33204348719592139440 * q^90 + 161045136122144660736 * q^91 - 932896292396925120 * q^92 - 107259275077774974528 * q^94 + 197187886676221266496 * q^96 + 77267514659308382822 * q^97 + 236544665851892453426 * q^98 - 342412845288286744966 * q^99

Decomposition of \(S_{21}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.21.c	\(\chi_{8}(7, \cdot)\)	None	0	1
8.21.d	\(\chi_{8}(3, \cdot)\)	8.21.d.a	1	1
		8.21.d.b	18

Decomposition of \(S_{21}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{21}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{21}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)