Space of modular forms of level 81 and weight 5

• Label: 81.5
• Level: 81
• Weight: 5
• Dimension: 740
• Nonzero newspaces: 4
• Newform subspaces: 9
• Sturm bound: 2430
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 81 = 3^{4} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(2430\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(81))\).

	Total	New	Old
Modular forms	1026	796	230
Cusp forms	918	740	178
Eisenstein series	108	56	52

Trace form

740 * q - 12 * q^2 - 18 * q^3 - 4 * q^4 - 21 * q^5 - 18 * q^6 - 59 * q^7 - 9 * q^8 - 18 * q^9 + 195 * q^10 + 474 * q^11 - 18 * q^12 - 245 * q^13 - 1155 * q^14 - 18 * q^15 - 760 * q^16 - 9 * q^17 - 2034 * q^18 - 545 * q^19 + 3333 * q^20 + 2277 * q^21 + 3504 * q^22 + 5703 * q^23 + 4734 * q^24 + 962 * q^25 - 27 * q^26 - 1449 * q^27 - 6089 * q^28 - 9003 * q^29 - 9522 * q^30 - 6113 * q^31 - 19314 * q^32 - 3231 * q^33 - 90 * q^34 + 5337 * q^35 + 10062 * q^36 + 7645 * q^37 + 13890 * q^38 - 18 * q^39 - 2229 * q^40 - 19164 * q^41 - 18333 * q^42 - 1868 * q^43 + 9063 * q^44 + 11214 * q^45 + 19959 * q^46 + 27933 * q^47 + 35127 * q^48 + 18504 * q^49 + 66900 * q^50 + 12330 * q^51 + 11125 * q^52 - 27 * q^53 - 13500 * q^54 - 19893 * q^55 - 78051 * q^56 - 21186 * q^57 - 34305 * q^58 - 55776 * q^59 - 58167 * q^60 - 24557 * q^61 - 76635 * q^62 - 14058 * q^63 - 12103 * q^64 + 36627 * q^65 + 99126 * q^66 + 2230 * q^67 + 115686 * q^68 + 20502 * q^69 + 40665 * q^70 - 19773 * q^71 - 138258 * q^72 + 16906 * q^73 - 21939 * q^74 - 56268 * q^75 + 55522 * q^76 - 28749 * q^77 - 44523 * q^78 + 7501 * q^79 + 11574 * q^81 - 11658 * q^82 + 15081 * q^83 + 153927 * q^84 - 52641 * q^85 + 21012 * q^86 + 125982 * q^87 - 133356 * q^88 - 102636 * q^89 - 1557 * q^90 - 62278 * q^91 - 25233 * q^92 + 3294 * q^93 + 33105 * q^94 + 86961 * q^95 - 37665 * q^96 + 119038 * q^97 + 271017 * q^98 + 4266 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(81))\)

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
81.5.b	\(\chi_{81}(80, \cdot)\)	81.5.b.a	6	1
		81.5.b.b	8
81.5.d	\(\chi_{81}(26, \cdot)\)	81.5.d.a	2	2
		81.5.d.b	4
		81.5.d.c	4
		81.5.d.d	4
		81.5.d.e	16
81.5.f	\(\chi_{81}(8, \cdot)\)	81.5.f.a	66	6
81.5.h	\(\chi_{81}(2, \cdot)\)	81.5.h.a	630	18

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(81))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(81)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)