Space of modular forms of level 27 and weight 6

• Label: 27.6
• Level: 27
• Weight: 6
• Dimension: 99
• Nonzero newspaces: 3
• Newform subspaces: 6
• Sturm bound: 324
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 27 = 3^{3} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(324\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(27))\).

	Total	New	Old
Modular forms	150	115	35
Cusp forms	120	99	21
Eisenstein series	30	16	14

Trace form

99 * q - 9 * q^2 - 6 * q^3 + 63 * q^4 - 171 * q^5 - 126 * q^6 + 129 * q^7 + 1323 * q^8 + 324 * q^9 + 39 * q^10 - 333 * q^11 - 2769 * q^12 - 2841 * q^13 - 3033 * q^14 + 1989 * q^15 + 6051 * q^16 + 7821 * q^17 - 99 * q^18 + 1134 * q^19 + 3303 * q^20 + 5424 * q^21 - 13269 * q^22 - 16560 * q^23 - 18486 * q^24 + 8820 * q^25 + 17082 * q^26 - 8109 * q^27 - 12726 * q^28 - 32436 * q^29 - 6453 * q^30 - 10977 * q^31 + 42489 * q^32 + 50634 * q^33 + 28971 * q^34 + 52092 * q^35 - 3600 * q^36 + 19170 * q^37 - 32931 * q^38 - 13971 * q^39 - 12477 * q^40 - 80325 * q^41 - 64422 * q^42 - 17133 * q^43 + 61227 * q^44 + 92493 * q^45 + 4089 * q^46 + 103617 * q^47 + 134049 * q^48 + 46860 * q^49 - 48456 * q^50 - 124866 * q^51 - 85881 * q^52 - 227358 * q^53 - 350946 * q^54 - 39444 * q^55 - 86067 * q^56 + 67767 * q^57 + 141963 * q^58 + 114408 * q^59 + 241290 * q^60 - 154869 * q^61 + 4302 * q^62 + 135981 * q^63 - 50607 * q^64 - 6669 * q^65 - 32931 * q^66 + 107814 * q^67 + 75024 * q^68 + 25263 * q^69 + 442059 * q^70 + 351387 * q^71 + 441684 * q^72 + 122679 * q^73 + 394011 * q^74 + 18399 * q^75 - 217737 * q^76 - 384669 * q^77 - 520974 * q^78 - 531033 * q^79 - 1048626 * q^80 - 428616 * q^81 - 360582 * q^82 - 488097 * q^83 - 522390 * q^84 - 235647 * q^85 + 132597 * q^86 + 304173 * q^87 + 750459 * q^88 + 606555 * q^89 + 327366 * q^90 + 309345 * q^91 + 1145025 * q^92 + 890079 * q^93 + 376791 * q^94 + 792783 * q^95 + 1165698 * q^96 - 189258 * q^97 + 405756 * q^98 - 28323 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.6.a	\(\chi_{27}(1, \cdot)\)	27.6.a.a	1	1
		27.6.a.b	2
		27.6.a.c	2
		27.6.a.d	2
27.6.c	\(\chi_{27}(10, \cdot)\)	27.6.c.a	8	2
27.6.e	\(\chi_{27}(4, \cdot)\)	27.6.e.a	84	6

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)