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Properties

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

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 7 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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

\( S_{8}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 1}\)