Properties

Label 27.8
Level 27
Weight 8
Dimension 141
Nonzero newspaces 3
Newforms 7
Sturm bound 432
Trace bound 1

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 7 \)
Sturm bound: \(432\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(27))\).

Total New Old
Modular forms 204 157 47
Cusp forms 174 141 33
Eisenstein series 30 16 14

Trace form

\( 141q + 3q^{2} - 6q^{3} + 159q^{4} - 39q^{5} + 1386q^{6} - 567q^{7} - 10533q^{8} - 1728q^{9} + O(q^{10}) \) \( 141q + 3q^{2} - 6q^{3} + 159q^{4} - 39q^{5} + 1386q^{6} - 567q^{7} - 10533q^{8} - 1728q^{9} + 10815q^{10} + 17859q^{11} - 10545q^{12} + 1611q^{13} + 32919q^{14} + 11709q^{15} - 26205q^{16} - 89523q^{17} - 156051q^{18} - 37950q^{19} + 281031q^{20} - 516q^{21} + 347691q^{22} - 92496q^{23} - 150894q^{24} - 219540q^{25} - 93270q^{26} + 114363q^{27} - 230550q^{28} + 522534q^{29} - 179901q^{30} + 765639q^{31} + 409401q^{32} - 31338q^{33} - 1903869q^{34} - 2661288q^{35} + 51264q^{36} - 154212q^{37} + 1807089q^{38} + 1919661q^{39} + 3792099q^{40} + 1958667q^{41} + 3792042q^{42} - 2114253q^{43} - 6374229q^{44} - 4430925q^{45} - 3439623q^{46} - 3552855q^{47} - 2424039q^{48} + 5526984q^{49} + 3979020q^{50} + 2918034q^{51} - 3373401q^{52} + 2796102q^{53} + 11971422q^{54} - 194124q^{55} + 7039389q^{56} - 284637q^{57} + 3516051q^{58} - 10478856q^{59} - 29390886q^{60} + 167607q^{61} - 8896818q^{62} + 3292389q^{63} - 7343103q^{64} + 18546015q^{65} + 39100653q^{66} + 8053002q^{67} + 17715816q^{68} - 12682935q^{69} - 8839725q^{70} - 20972277q^{71} - 33138540q^{72} - 112029q^{73} - 46124589q^{74} - 26317941q^{75} - 24410553q^{76} + 4992927q^{77} + 36593658q^{78} + 52766847q^{79} + 139153038q^{80} + 45736524q^{81} + 36224610q^{82} - 6457353q^{83} - 27588054q^{84} - 43436547q^{85} - 105133395q^{86} - 55384731q^{87} - 39536517q^{88} - 30017349q^{89} - 25256970q^{90} - 17105319q^{91} + 34715121q^{92} + 69808065q^{93} + 26495823q^{94} + 22119375q^{95} + 33014034q^{96} + 71883540q^{97} + 7340040q^{98} - 111262167q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(27))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
27.8.a \(\chi_{27}(1, \cdot)\) 27.8.a.a 1 1
27.8.a.b 2
27.8.a.c 2
27.8.a.d 2
27.8.a.e 2
27.8.c \(\chi_{27}(10, \cdot)\) 27.8.c.a 12 2
27.8.e \(\chi_{27}(4, \cdot)\) 27.8.e.a 120 6

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)