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Properties

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

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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

\( 184 q - 21 q^{2} - 6 q^{3} + 1615 q^{4} + 1929 q^{5} - 6822 q^{6} + 2591 q^{7} + 51339 q^{8} + 2538 q^{9} + O(q^{10}) \) \( 184 q - 21 q^{2} - 6 q^{3} + 1615 q^{4} + 1929 q^{5} - 6822 q^{6} + 2591 q^{7} + 51339 q^{8} + 2538 q^{9} - 100881 q^{10} - 220917 q^{11} + 319935 q^{12} + 299915 q^{13} - 1115241 q^{14} - 706356 q^{15} + 1026211 q^{16} + 1833327 q^{17} + 922437 q^{18} - 385831 q^{19} - 10303737 q^{20} - 3497394 q^{21} + 475083 q^{22} + 8251923 q^{23} + 7959258 q^{24} + 3302095 q^{25} - 35565990 q^{26} - 3148155 q^{27} + 13960394 q^{28} + 20966289 q^{29} + 21174507 q^{30} - 22903021 q^{31} - 43311015 q^{32} - 19055889 q^{33} + 13962771 q^{34} + 65516217 q^{35} + 137733552 q^{36} + 17758655 q^{37} - 131512263 q^{38} - 89330160 q^{39} - 140494077 q^{40} - 87874539 q^{41} + 227141658 q^{42} + 135473471 q^{43} + 333511467 q^{44} - 78992532 q^{45} - 67681287 q^{46} - 189784497 q^{47} + 248865393 q^{48} - 193273341 q^{49} - 387617916 q^{50} - 101541537 q^{51} + 462987719 q^{52} + 530357580 q^{53} - 315431874 q^{54} + 13865616 q^{55} - 562110771 q^{56} - 103852992 q^{57} - 1087432029 q^{58} + 230316780 q^{59} + 1127571210 q^{60} + 759685067 q^{61} + 858573966 q^{62} - 419972706 q^{63} - 409491023 q^{64} - 1334817669 q^{65} + 472205277 q^{66} - 850870927 q^{67} - 1424295792 q^{68} - 1234413090 q^{69} + 192054339 q^{70} + 2180480031 q^{71} + 2831326452 q^{72} + 894387311 q^{73} - 183851421 q^{74} - 226667796 q^{75} - 1162091449 q^{76} - 1685806899 q^{77} - 1247881230 q^{78} - 847798489 q^{79} + 430711374 q^{80} - 392600970 q^{81} - 2399211054 q^{82} - 1473871575 q^{83} + 1027656618 q^{84} + 2377527543 q^{85} + 1503257565 q^{86} + 2687612040 q^{87} + 4862077371 q^{88} + 5092038504 q^{89} + 7127326206 q^{90} + 366635383 q^{91} - 6819831519 q^{92} - 7299151842 q^{93} - 4121762337 q^{94} - 8608868517 q^{95} - 2644638174 q^{96} + 3691766807 q^{97} + 2073739608 q^{98} + 5248107342 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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