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Properties

Label 9.5
Level 9
Weight 5
Dimension 8
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 30
Trace bound 1

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(9))\).

Total New Old
Modular forms 16 12 4
Cusp forms 8 8 0
Eisenstein series 8 4 4

Trace form

\( 8 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 12 q^{5} - 99 q^{6} - 44 q^{7} + 99 q^{9} + O(q^{10}) \) \( 8 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 12 q^{5} - 99 q^{6} - 44 q^{7} + 99 q^{9} + 216 q^{10} + 483 q^{11} + 330 q^{12} - 230 q^{13} - 1146 q^{14} - 1026 q^{15} - 553 q^{16} + 1404 q^{18} + 862 q^{19} + 1614 q^{20} + 480 q^{21} - 513 q^{22} - 282 q^{23} - 1449 q^{24} - 787 q^{25} + 54 q^{27} + 1420 q^{28} - 1056 q^{29} - 1278 q^{30} + 562 q^{31} - 1161 q^{32} + 279 q^{33} + 1269 q^{34} - 2385 q^{36} - 1640 q^{37} - 789 q^{38} + 1974 q^{39} + 2214 q^{40} + 7629 q^{41} + 9612 q^{42} + 3187 q^{43} - 4212 q^{45} - 12528 q^{46} - 9642 q^{47} - 6771 q^{48} - 5097 q^{49} + 3027 q^{50} + 2457 q^{51} + 208 q^{52} - 405 q^{54} + 3024 q^{55} - 462 q^{56} + 5367 q^{57} + 14850 q^{58} + 6225 q^{59} + 7470 q^{60} + 8866 q^{61} - 7578 q^{63} + 8522 q^{64} - 7158 q^{65} - 13734 q^{66} - 12623 q^{67} - 10503 q^{68} - 13878 q^{69} - 16740 q^{70} + 8451 q^{72} - 1406 q^{73} + 26454 q^{74} + 21021 q^{75} - 6287 q^{76} + 2580 q^{77} - 12060 q^{78} - 3788 q^{79} + 18387 q^{81} + 5670 q^{82} - 1866 q^{83} - 6486 q^{84} + 7074 q^{85} - 37731 q^{86} - 21564 q^{87} + 12771 q^{88} + 20790 q^{90} + 41108 q^{91} + 33636 q^{92} + 19254 q^{93} - 1620 q^{94} - 13362 q^{95} - 3672 q^{96} - 40607 q^{97} - 9126 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)

We only show spaces with odd 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
9.5.b \(\chi_{9}(8, \cdot)\) 9.5.b.a 2 1
9.5.d \(\chi_{9}(2, \cdot)\) 9.5.d.a 6 2