Space of modular forms of level 8 and weight 8

• Label: 8.8
• Level: 8
• Weight: 8
• Dimension: 8
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 32
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 8 = 2^{3} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	17	10	7
Cusp forms	11	8	3
Eisenstein series	6	2	4

Trace form

8 * q + 6 * q^2 - 40 * q^3 + 116 * q^4 + 348 * q^5 + 268 * q^6 - 2368 * q^7 + 1512 * q^8 + 1700 * q^9 - 1656 * q^10 - 5688 * q^11 - 4088 * q^12 - 4660 * q^13 + 12048 * q^14 + 43680 * q^15 + 35344 * q^16 - 25968 * q^17 - 89062 * q^18 - 1352 * q^19 - 114768 * q^20 - 15552 * q^21 + 152860 * q^22 + 81984 * q^23 + 282512 * q^24 - 3940 * q^25 - 316968 * q^26 - 332560 * q^27 - 480800 * q^28 + 222636 * q^29 + 821648 * q^30 + 121600 * q^31 + 817056 * q^32 + 126680 * q^33 - 1009108 * q^34 - 488928 * q^35 - 1253556 * q^36 - 471780 * q^37 + 974124 * q^38 + 846336 * q^39 + 954464 * q^40 + 343248 * q^41 - 1093088 * q^42 + 20360 * q^43 - 1096344 * q^44 - 507188 * q^45 + 929840 * q^46 + 1168512 * q^47 + 853920 * q^48 - 452024 * q^49 - 148626 * q^50 + 220720 * q^51 + 823952 * q^52 + 2109180 * q^53 - 1077064 * q^54 - 4423808 * q^55 - 2468928 * q^56 - 2477256 * q^57 + 3130744 * q^58 - 1863576 * q^59 + 5715168 * q^60 + 1002860 * q^61 - 7055808 * q^62 + 3863776 * q^63 - 4792768 * q^64 + 4931016 * q^65 + 7926264 * q^66 + 7625560 * q^67 + 6608040 * q^68 - 6793792 * q^69 - 7406912 * q^70 - 12856128 * q^71 - 11363944 * q^72 - 5261616 * q^73 + 7744200 * q^74 + 10695784 * q^75 + 9241288 * q^76 + 5023680 * q^77 - 9471184 * q^78 + 14929792 * q^79 - 12600384 * q^80 + 3381600 * q^81 + 10715932 * q^82 - 6949320 * q^83 + 4220608 * q^84 - 6081800 * q^85 - 5639076 * q^86 - 40431936 * q^87 + 1541200 * q^88 + 7301712 * q^89 - 121864 * q^90 - 2573664 * q^91 + 669600 * q^92 + 14460160 * q^93 + 15503712 * q^94 + 45845088 * q^95 + 21402176 * q^96 + 3777552 * q^97 - 14983242 * q^98 - 11495192 * q^99

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

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
8.8.a	\(\chi_{8}(1, \cdot)\)	8.8.a.a	1	1
		8.8.a.b	1
8.8.b	\(\chi_{8}(5, \cdot)\)	8.8.b.a	6	1

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

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