Space of modular forms of level 27 and weight 3

• Label: 27.3
• Level: 27
• Weight: 3
• Dimension: 35
• Nonzero newspaces: 3
• Newform subspaces: 4
• Sturm bound: 162
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 27 = 3^{3} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(162\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(27))\).

	Total	New	Old
Modular forms	69	51	18
Cusp forms	39	35	4
Eisenstein series	30	16	14

Trace form

35 * q - 3 * q^2 - 6 * q^3 - 13 * q^4 - 21 * q^5 - 18 * q^6 - 11 * q^7 - 9 * q^8 + 3 * q^10 - 3 * q^11 - 15 * q^12 - 23 * q^13 - 21 * q^14 - 9 * q^15 - 13 * q^16 - 9 * q^17 + 63 * q^18 - 2 * q^19 + 219 * q^20 + 132 * q^21 + 51 * q^22 + 168 * q^23 + 144 * q^24 + 29 * q^25 - 90 * q^27 - 110 * q^28 - 246 * q^29 - 243 * q^30 - 41 * q^31 - 387 * q^32 - 207 * q^33 - 81 * q^34 - 252 * q^35 - 360 * q^36 + 16 * q^37 - 51 * q^38 + 15 * q^39 - 21 * q^40 + 249 * q^41 + 486 * q^42 + 43 * q^43 + 639 * q^44 + 477 * q^45 + 165 * q^46 + 483 * q^47 + 453 * q^48 + 39 * q^49 + 264 * q^50 + 36 * q^51 + 91 * q^52 - 54 * q^54 - 114 * q^55 - 363 * q^56 - 192 * q^57 - 129 * q^58 - 561 * q^59 - 846 * q^60 - 191 * q^61 - 900 * q^62 - 585 * q^63 + 53 * q^64 - 435 * q^65 - 423 * q^66 + 256 * q^67 + 126 * q^68 + 99 * q^69 + 591 * q^70 + 315 * q^71 + 720 * q^72 + 97 * q^73 + 219 * q^74 + 255 * q^75 + 451 * q^76 + 195 * q^77 + 180 * q^78 + 151 * q^79 + 36 * q^81 - 330 * q^82 + 51 * q^83 - 588 * q^84 - 207 * q^85 - 75 * q^86 - 279 * q^87 - 717 * q^88 + 72 * q^89 + 288 * q^90 - 7 * q^91 - 51 * q^92 + 591 * q^93 - 741 * q^94 + 615 * q^95 + 270 * q^96 - 470 * q^97 + 882 * q^98 + 513 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.3.b	\(\chi_{27}(26, \cdot)\)	27.3.b.a	1	1
		27.3.b.b	2
27.3.d	\(\chi_{27}(8, \cdot)\)	27.3.d.a	2	2
27.3.f	\(\chi_{27}(2, \cdot)\)	27.3.f.a	30	6

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

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