Space of modular forms of level 27 and weight 8

• Label: 27.8
• Level: 27
• Weight: 8
• Dimension: 141
• Nonzero newspaces: 3
• Newform subspaces: 7
• Sturm bound: 432
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 27 = 3^{3} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(432\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(27))\).

	Total	New	Old
Modular forms	204	157	47
Cusp forms	174	141	33
Eisenstein series	30	16	14

Trace form

141 * q + 3 * q^2 - 6 * q^3 + 159 * q^4 - 39 * q^5 + 1386 * q^6 - 567 * q^7 - 10533 * q^8 - 1728 * q^9 + 10815 * q^10 + 17859 * q^11 - 10545 * q^12 + 1611 * q^13 + 32919 * q^14 + 11709 * q^15 - 26205 * q^16 - 89523 * q^17 - 156051 * q^18 - 37950 * q^19 + 281031 * q^20 - 516 * q^21 + 347691 * q^22 - 92496 * q^23 - 150894 * q^24 - 219540 * q^25 - 93270 * q^26 + 114363 * q^27 - 230550 * q^28 + 522534 * q^29 - 179901 * q^30 + 765639 * q^31 + 409401 * q^32 - 31338 * q^33 - 1903869 * q^34 - 2661288 * q^35 + 51264 * q^36 - 154212 * q^37 + 1807089 * q^38 + 1919661 * q^39 + 3792099 * q^40 + 1958667 * q^41 + 3792042 * q^42 - 2114253 * q^43 - 6374229 * q^44 - 4430925 * q^45 - 3439623 * q^46 - 3552855 * q^47 - 2424039 * q^48 + 5526984 * q^49 + 3979020 * q^50 + 2918034 * q^51 - 3373401 * q^52 + 2796102 * q^53 + 11971422 * q^54 - 194124 * q^55 + 7039389 * q^56 - 284637 * q^57 + 3516051 * q^58 - 10478856 * q^59 - 29390886 * q^60 + 167607 * q^61 - 8896818 * q^62 + 3292389 * q^63 - 7343103 * q^64 + 18546015 * q^65 + 39100653 * q^66 + 8053002 * q^67 + 17715816 * q^68 - 12682935 * q^69 - 8839725 * q^70 - 20972277 * q^71 - 33138540 * q^72 - 112029 * q^73 - 46124589 * q^74 - 26317941 * q^75 - 24410553 * q^76 + 4992927 * q^77 + 36593658 * q^78 + 52766847 * q^79 + 139153038 * q^80 + 45736524 * q^81 + 36224610 * q^82 - 6457353 * q^83 - 27588054 * q^84 - 43436547 * q^85 - 105133395 * q^86 - 55384731 * q^87 - 39536517 * q^88 - 30017349 * q^89 - 25256970 * q^90 - 17105319 * q^91 + 34715121 * q^92 + 69808065 * q^93 + 26495823 * q^94 + 22119375 * q^95 + 33014034 * q^96 + 71883540 * q^97 + 7340040 * q^98 - 111262167 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.8.a	\(\chi_{27}(1, \cdot)\)	27.8.a.a	1	1
		27.8.a.b	2
		27.8.a.c	2
		27.8.a.d	2
		27.8.a.e	2
27.8.c	\(\chi_{27}(10, \cdot)\)	27.8.c.a	12	2
27.8.e	\(\chi_{27}(4, \cdot)\)	27.8.e.a	120	6

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)