Space of modular forms of level 27 and weight 10

• Label: 27.10
• Level: 27
• Weight: 10
• Dimension: 184
• Nonzero newspaces: 3
• Newform subspaces: 6
• Sturm bound: 540
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 27 = 3^{3} \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(540\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(27))\).

	Total	New	Old
Modular forms	258	200	58
Cusp forms	228	184	44
Eisenstein series	30	16	14

Trace form

184 * q - 21 * q^2 - 6 * q^3 + 1615 * q^4 + 1929 * q^5 - 6822 * q^6 + 2591 * q^7 + 51339 * q^8 + 2538 * q^9 - 100881 * q^10 - 220917 * q^11 + 319935 * q^12 + 299915 * q^13 - 1115241 * q^14 - 706356 * q^15 + 1026211 * q^16 + 1833327 * q^17 + 922437 * q^18 - 385831 * q^19 - 10303737 * q^20 - 3497394 * q^21 + 475083 * q^22 + 8251923 * q^23 + 7959258 * q^24 + 3302095 * q^25 - 35565990 * q^26 - 3148155 * q^27 + 13960394 * q^28 + 20966289 * q^29 + 21174507 * q^30 - 22903021 * q^31 - 43311015 * q^32 - 19055889 * q^33 + 13962771 * q^34 + 65516217 * q^35 + 137733552 * q^36 + 17758655 * q^37 - 131512263 * q^38 - 89330160 * q^39 - 140494077 * q^40 - 87874539 * q^41 + 227141658 * q^42 + 135473471 * q^43 + 333511467 * q^44 - 78992532 * q^45 - 67681287 * q^46 - 189784497 * q^47 + 248865393 * q^48 - 193273341 * q^49 - 387617916 * q^50 - 101541537 * q^51 + 462987719 * q^52 + 530357580 * q^53 - 315431874 * q^54 + 13865616 * q^55 - 562110771 * q^56 - 103852992 * q^57 - 1087432029 * q^58 + 230316780 * q^59 + 1127571210 * q^60 + 759685067 * q^61 + 858573966 * q^62 - 419972706 * q^63 - 409491023 * q^64 - 1334817669 * q^65 + 472205277 * q^66 - 850870927 * q^67 - 1424295792 * q^68 - 1234413090 * q^69 + 192054339 * q^70 + 2180480031 * q^71 + 2831326452 * q^72 + 894387311 * q^73 - 183851421 * q^74 - 226667796 * q^75 - 1162091449 * q^76 - 1685806899 * q^77 - 1247881230 * q^78 - 847798489 * q^79 + 430711374 * q^80 - 392600970 * q^81 - 2399211054 * q^82 - 1473871575 * q^83 + 1027656618 * q^84 + 2377527543 * q^85 + 1503257565 * q^86 + 2687612040 * q^87 + 4862077371 * q^88 + 5092038504 * q^89 + 7127326206 * q^90 + 366635383 * q^91 - 6819831519 * q^92 - 7299151842 * q^93 - 4121762337 * q^94 - 8608868517 * q^95 - 2644638174 * q^96 + 3691766807 * q^97 + 2073739608 * q^98 + 5248107342 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.10.a	\(\chi_{27}(1, \cdot)\)	27.10.a.a	2	1
		27.10.a.b	3
		27.10.a.c	3
		27.10.a.d	4
27.10.c	\(\chi_{27}(10, \cdot)\)	27.10.c.a	16	2
27.10.e	\(\chi_{27}(4, \cdot)\)	27.10.e.a	156	6

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)