Space of modular forms of level 27 and weight 5

• Label: 27.5
• Level: 27
• Weight: 5
• Dimension: 77
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 270
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 27 = 3^{3} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(270\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(27))\).

	Total	New	Old
Modular forms	123	93	30
Cusp forms	93	77	16
Eisenstein series	30	16	14

Trace form

77 * q - 3 * q^2 - 6 * q^3 - 37 * q^4 + 15 * q^5 + 90 * q^6 + 73 * q^7 - 9 * q^8 - 108 * q^9 - 453 * q^10 - 975 * q^11 - 339 * q^12 + 445 * q^13 + 2283 * q^14 + 1017 * q^15 + 1187 * q^16 - 9 * q^17 + 603 * q^18 - 1052 * q^19 - 4101 * q^20 - 2784 * q^21 - 1005 * q^22 - 2442 * q^23 - 3312 * q^24 + 677 * q^25 + 1368 * q^27 + 874 * q^28 + 6072 * q^29 + 10773 * q^30 + 2191 * q^31 + 11385 * q^32 + 2925 * q^33 - 1881 * q^34 - 2682 * q^35 - 7704 * q^36 - 1394 * q^37 - 5775 * q^38 - 1983 * q^39 - 2229 * q^40 - 1875 * q^41 + 8694 * q^42 - 3869 * q^43 - 4545 * q^44 - 7029 * q^45 + 8781 * q^46 + 483 * q^47 - 28383 * q^48 - 1629 * q^49 - 38004 * q^50 - 14814 * q^51 - 5753 * q^52 + 13878 * q^54 + 5370 * q^55 + 39705 * q^56 + 15792 * q^57 - 5145 * q^58 + 18537 * q^59 + 50670 * q^60 - 1043 * q^61 + 38304 * q^62 + 21609 * q^63 + 11669 * q^64 + 30885 * q^65 + 11349 * q^66 + 30082 * q^67 - 33030 * q^68 - 26847 * q^69 - 16845 * q^70 - 19773 * q^71 - 77580 * q^72 - 33875 * q^73 - 101301 * q^74 - 49155 * q^75 - 62417 * q^76 - 36489 * q^77 - 9108 * q^78 - 6569 * q^79 - 12600 * q^81 + 23190 * q^82 + 20679 * q^83 + 82356 * q^84 + 54837 * q^85 + 134205 * q^86 + 84555 * q^87 + 120075 * q^88 + 110232 * q^89 + 153540 * q^90 - 3379 * q^91 + 39909 * q^92 + 1293 * q^93 - 20193 * q^94 - 51801 * q^95 - 152226 * q^96 - 42236 * q^97 - 259938 * q^98 - 162405 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.5.b	\(\chi_{27}(26, \cdot)\)	27.5.b.a	1	1
		27.5.b.b	2
		27.5.b.c	2
27.5.d	\(\chi_{27}(8, \cdot)\)	27.5.d.a	6	2
27.5.f	\(\chi_{27}(2, \cdot)\)	27.5.f.a	66	6

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)