Space of modular forms of level 27 and weight 12

• Label: 27.12
• Level: 27
• Weight: 12
• Dimension: 227
• Nonzero newspaces: 3
• Newform subspaces: 7
• Sturm bound: 648
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 27 = 3^{3} \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(648\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(27))\).

	Total	New	Old
Modular forms	312	243	69
Cusp forms	282	227	55
Eisenstein series	30	16	14

Trace form

227 * q + 27 * q^2 - 6 * q^3 + 5183 * q^4 + 10161 * q^5 + 4410 * q^6 - 10175 * q^7 - 265797 * q^8 + 96228 * q^9 + 523695 * q^10 - 1481517 * q^11 + 323823 * q^12 - 3974669 * q^13 + 9164727 * q^14 + 3836529 * q^15 + 9355427 * q^16 - 44804079 * q^17 + 8396685 * q^18 + 35499226 * q^19 + 68129991 * q^20 + 73765320 * q^21 - 130442133 * q^22 - 85241340 * q^23 - 52250526 * q^24 + 112907570 * q^25 - 409760118 * q^26 + 406211103 * q^27 + 111489322 * q^28 - 792926496 * q^29 - 845653581 * q^30 + 147783943 * q^31 + 2369510649 * q^32 + 792631584 * q^33 - 408530061 * q^34 - 1808051688 * q^35 - 1271261664 * q^36 - 477224978 * q^37 - 689128695 * q^38 + 2330844945 * q^39 + 4740734499 * q^40 + 2031453207 * q^41 - 3110154678 * q^42 - 3295979285 * q^43 - 7060264533 * q^44 + 9102254625 * q^45 + 1190918649 * q^46 + 2790889209 * q^47 - 6384109047 * q^48 + 7128691950 * q^49 - 12703460940 * q^50 + 1310770386 * q^51 - 14399297561 * q^52 - 7846272918 * q^53 + 22629480894 * q^54 + 1169860476 * q^55 + 19654814205 * q^56 - 32645841267 * q^57 + 13154592867 * q^58 + 48436639524 * q^59 + 50690195514 * q^60 - 23079382313 * q^61 - 79221602610 * q^62 - 30632962095 * q^63 - 66521865247 * q^64 + 43320653775 * q^65 + 38229021261 * q^66 + 24676647850 * q^67 + 159667457976 * q^68 - 30801215529 * q^69 - 74848805085 * q^70 - 172317366837 * q^71 + 3848431572 * q^72 - 64437276389 * q^73 + 36884774403 * q^74 + 108769340739 * q^75 + 187005848839 * q^76 + 150839725059 * q^77 - 72959471478 * q^78 - 48645389345 * q^79 - 374429152242 * q^80 - 144648556128 * q^81 - 26559994830 * q^82 + 212542492959 * q^83 + 273199455402 * q^84 + 248593960233 * q^85 + 185452685181 * q^86 - 308647046223 * q^87 - 654414711045 * q^88 - 577567364355 * q^89 + 650525024790 * q^90 - 60790260775 * q^91 + 431940843729 * q^92 - 323782133601 * q^93 + 321928551807 * q^94 + 768694890015 * q^95 + 620032058802 * q^96 - 200427663974 * q^97 - 1027484216352 * q^98 - 581308635231 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.12.a	\(\chi_{27}(1, \cdot)\)	27.12.a.a	1	1
		27.12.a.b	2
		27.12.a.c	4
		27.12.a.d	4
		27.12.a.e	4
27.12.c	\(\chi_{27}(10, \cdot)\)	27.12.c.a	20	2
27.12.e	\(\chi_{27}(4, \cdot)\)	27.12.e.a	192	6

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)