Space of modular forms of level 27 and weight 4

• Label: 27.4
• Level: 27
• Weight: 4
• Dimension: 56
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 216
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 27 = 3^{3} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(216\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(27))\).

	Total	New	Old
Modular forms	96	72	24
Cusp forms	66	56	10
Eisenstein series	30	16	14

Trace form

56 * q - 3 * q^2 - 6 * q^3 + 11 * q^4 + 21 * q^5 - 18 * q^6 - 41 * q^7 - 141 * q^8 - 54 * q^9 - 45 * q^10 + 123 * q^11 + 147 * q^12 + 103 * q^13 + 111 * q^14 - 36 * q^15 - 205 * q^16 - 405 * q^17 - 639 * q^18 - 95 * q^19 - 609 * q^20 - 138 * q^21 + 27 * q^22 + 435 * q^23 + 1170 * q^24 + 425 * q^25 + 2442 * q^26 + 1125 * q^27 + 490 * q^28 + 429 * q^29 + 459 * q^30 - 437 * q^31 - 1071 * q^32 - 639 * q^33 - 9 * q^34 - 1263 * q^35 - 2088 * q^36 - 797 * q^37 - 2085 * q^38 - 768 * q^39 - 621 * q^40 - 1599 * q^41 - 3078 * q^42 + 175 * q^43 - 1749 * q^44 - 360 * q^45 + 873 * q^46 + 1383 * q^47 + 2289 * q^48 + 33 * q^49 + 3930 * q^50 + 2655 * q^51 - 41 * q^52 + 2628 * q^53 + 5454 * q^54 + 216 * q^55 + 5973 * q^56 + 3426 * q^57 + 1647 * q^58 + 3036 * q^59 + 1314 * q^60 + 391 * q^61 - 2346 * q^62 - 2610 * q^63 - 2239 * q^64 - 6825 * q^65 - 11115 * q^66 - 3191 * q^67 - 10476 * q^68 - 6138 * q^69 - 4185 * q^70 - 5841 * q^71 - 36 * q^72 + 715 * q^73 + 4359 * q^74 + 2604 * q^75 + 5539 * q^76 + 4557 * q^77 + 6066 * q^78 + 3631 * q^79 + 9678 * q^80 + 3438 * q^81 + 1134 * q^82 + 4281 * q^83 + 7674 * q^84 + 5823 * q^85 + 3657 * q^86 + 2880 * q^87 + 2547 * q^88 - 4410 * q^89 - 12510 * q^90 - 1657 * q^91 - 19311 * q^92 - 11802 * q^93 - 9045 * q^94 - 10245 * q^95 - 14094 * q^96 - 4685 * q^97 - 3546 * q^98 - 1242 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.4.a	\(\chi_{27}(1, \cdot)\)	27.4.a.a	1	1
		27.4.a.b	1
		27.4.a.c	2
27.4.c	\(\chi_{27}(10, \cdot)\)	27.4.c.a	4	2
27.4.e	\(\chi_{27}(4, \cdot)\)	27.4.e.a	48	6

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

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