↑

Properties

Label 27.4
Level 27
Weight 4
Dimension 56
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 216
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(216\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(27))\).

Total New Old
Modular forms 96 72 24
Cusp forms 66 56 10
Eisenstein series 30 16 14

Trace form

\( 56 q - 3 q^{2} - 6 q^{3} + 11 q^{4} + 21 q^{5} - 18 q^{6} - 41 q^{7} - 141 q^{8} - 54 q^{9} + O(q^{10}) \) \( 56 q - 3 q^{2} - 6 q^{3} + 11 q^{4} + 21 q^{5} - 18 q^{6} - 41 q^{7} - 141 q^{8} - 54 q^{9} - 45 q^{10} + 123 q^{11} + 147 q^{12} + 103 q^{13} + 111 q^{14} - 36 q^{15} - 205 q^{16} - 405 q^{17} - 639 q^{18} - 95 q^{19} - 609 q^{20} - 138 q^{21} + 27 q^{22} + 435 q^{23} + 1170 q^{24} + 425 q^{25} + 2442 q^{26} + 1125 q^{27} + 490 q^{28} + 429 q^{29} + 459 q^{30} - 437 q^{31} - 1071 q^{32} - 639 q^{33} - 9 q^{34} - 1263 q^{35} - 2088 q^{36} - 797 q^{37} - 2085 q^{38} - 768 q^{39} - 621 q^{40} - 1599 q^{41} - 3078 q^{42} + 175 q^{43} - 1749 q^{44} - 360 q^{45} + 873 q^{46} + 1383 q^{47} + 2289 q^{48} + 33 q^{49} + 3930 q^{50} + 2655 q^{51} - 41 q^{52} + 2628 q^{53} + 5454 q^{54} + 216 q^{55} + 5973 q^{56} + 3426 q^{57} + 1647 q^{58} + 3036 q^{59} + 1314 q^{60} + 391 q^{61} - 2346 q^{62} - 2610 q^{63} - 2239 q^{64} - 6825 q^{65} - 11115 q^{66} - 3191 q^{67} - 10476 q^{68} - 6138 q^{69} - 4185 q^{70} - 5841 q^{71} - 36 q^{72} + 715 q^{73} + 4359 q^{74} + 2604 q^{75} + 5539 q^{76} + 4557 q^{77} + 6066 q^{78} + 3631 q^{79} + 9678 q^{80} + 3438 q^{81} + 1134 q^{82} + 4281 q^{83} + 7674 q^{84} + 5823 q^{85} + 3657 q^{86} + 2880 q^{87} + 2547 q^{88} - 4410 q^{89} - 12510 q^{90} - 1657 q^{91} - 19311 q^{92} - 11802 q^{93} - 9045 q^{94} - 10245 q^{95} - 14094 q^{96} - 4685 q^{97} - 3546 q^{98} - 1242 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.4.a \(\chi_{27}(1, \cdot)\) 27.4.a.a 1 1
27.4.a.b 1
27.4.a.c 2
27.4.c \(\chi_{27}(10, \cdot)\) 27.4.c.a 4 2
27.4.e \(\chi_{27}(4, \cdot)\) 27.4.e.a 48 6

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

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