Properties

Label 9.5.d
Level 9
Weight 5
Character orbit d
Rep. character \(\chi_{9}(2,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 6
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 9.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(9, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

\(6q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 99q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 99q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 99q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 99q^{9} \) \(\mathstrut -\mathstrut 36q^{10} \) \(\mathstrut +\mathstrut 483q^{11} \) \(\mathstrut +\mathstrut 330q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 1146q^{14} \) \(\mathstrut -\mathstrut 1026q^{15} \) \(\mathstrut +\mathstrut 15q^{16} \) \(\mathstrut +\mathstrut 1404q^{18} \) \(\mathstrut -\mathstrut 258q^{19} \) \(\mathstrut +\mathstrut 1614q^{20} \) \(\mathstrut +\mathstrut 480q^{21} \) \(\mathstrut -\mathstrut 369q^{22} \) \(\mathstrut -\mathstrut 282q^{23} \) \(\mathstrut -\mathstrut 1449q^{24} \) \(\mathstrut -\mathstrut 273q^{25} \) \(\mathstrut +\mathstrut 54q^{27} \) \(\mathstrut +\mathstrut 1308q^{28} \) \(\mathstrut -\mathstrut 1056q^{29} \) \(\mathstrut -\mathstrut 1278q^{30} \) \(\mathstrut +\mathstrut 1290q^{31} \) \(\mathstrut -\mathstrut 1161q^{32} \) \(\mathstrut +\mathstrut 279q^{33} \) \(\mathstrut +\mathstrut 513q^{34} \) \(\mathstrut -\mathstrut 2385q^{36} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 789q^{38} \) \(\mathstrut +\mathstrut 1974q^{39} \) \(\mathstrut -\mathstrut 1314q^{40} \) \(\mathstrut +\mathstrut 7629q^{41} \) \(\mathstrut +\mathstrut 9612q^{42} \) \(\mathstrut -\mathstrut 285q^{43} \) \(\mathstrut -\mathstrut 4212q^{45} \) \(\mathstrut -\mathstrut 5760q^{46} \) \(\mathstrut -\mathstrut 9642q^{47} \) \(\mathstrut -\mathstrut 6771q^{48} \) \(\mathstrut -\mathstrut 1863q^{49} \) \(\mathstrut +\mathstrut 3027q^{50} \) \(\mathstrut +\mathstrut 2457q^{51} \) \(\mathstrut -\mathstrut 240q^{52} \) \(\mathstrut -\mathstrut 405q^{54} \) \(\mathstrut +\mathstrut 2016q^{55} \) \(\mathstrut -\mathstrut 462q^{56} \) \(\mathstrut +\mathstrut 5367q^{57} \) \(\mathstrut +\mathstrut 6462q^{58} \) \(\mathstrut +\mathstrut 6225q^{59} \) \(\mathstrut +\mathstrut 7470q^{60} \) \(\mathstrut +\mathstrut 3630q^{61} \) \(\mathstrut -\mathstrut 7578q^{63} \) \(\mathstrut +\mathstrut 15450q^{64} \) \(\mathstrut -\mathstrut 7158q^{65} \) \(\mathstrut -\mathstrut 13734q^{66} \) \(\mathstrut -\mathstrut 5055q^{67} \) \(\mathstrut -\mathstrut 10503q^{68} \) \(\mathstrut -\mathstrut 13878q^{69} \) \(\mathstrut -\mathstrut 9684q^{70} \) \(\mathstrut +\mathstrut 8451q^{72} \) \(\mathstrut -\mathstrut 14622q^{73} \) \(\mathstrut +\mathstrut 26454q^{74} \) \(\mathstrut +\mathstrut 21021q^{75} \) \(\mathstrut -\mathstrut 4047q^{76} \) \(\mathstrut +\mathstrut 2580q^{77} \) \(\mathstrut -\mathstrut 12060q^{78} \) \(\mathstrut +\mathstrut 4764q^{79} \) \(\mathstrut +\mathstrut 18387q^{81} \) \(\mathstrut -\mathstrut 9702q^{82} \) \(\mathstrut -\mathstrut 1866q^{83} \) \(\mathstrut -\mathstrut 6486q^{84} \) \(\mathstrut +\mathstrut 12366q^{85} \) \(\mathstrut -\mathstrut 37731q^{86} \) \(\mathstrut -\mathstrut 21564q^{87} \) \(\mathstrut +\mathstrut 14787q^{88} \) \(\mathstrut +\mathstrut 20790q^{90} \) \(\mathstrut +\mathstrut 34836q^{91} \) \(\mathstrut +\mathstrut 33636q^{92} \) \(\mathstrut +\mathstrut 19254q^{93} \) \(\mathstrut -\mathstrut 12708q^{94} \) \(\mathstrut -\mathstrut 13362q^{95} \) \(\mathstrut -\mathstrut 3672q^{96} \) \(\mathstrut -\mathstrut 28959q^{97} \) \(\mathstrut -\mathstrut 9126q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(9, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
9.5.d.a \(6\) \(0.930\) 6.0.39400128.1 None \(-3\) \(-3\) \(-12\) \(12\) \(q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots\)