Properties

Label 5.6.b
Level 5
Weight 6
Character orbit b
Rep. character \(\chi_{5}(4,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(5, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

Trace form

\(2q \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 90q^{5} \) \(\mathstrut +\mathstrut 264q^{6} \) \(\mathstrut -\mathstrut 306q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 90q^{5} \) \(\mathstrut +\mathstrut 264q^{6} \) \(\mathstrut -\mathstrut 306q^{9} \) \(\mathstrut -\mathstrut 440q^{10} \) \(\mathstrut +\mathstrut 504q^{11} \) \(\mathstrut +\mathstrut 792q^{14} \) \(\mathstrut +\mathstrut 1320q^{15} \) \(\mathstrut -\mathstrut 2528q^{16} \) \(\mathstrut -\mathstrut 440q^{19} \) \(\mathstrut +\mathstrut 1080q^{20} \) \(\mathstrut -\mathstrut 2376q^{21} \) \(\mathstrut +\mathstrut 5280q^{24} \) \(\mathstrut +\mathstrut 1850q^{25} \) \(\mathstrut +\mathstrut 1584q^{26} \) \(\mathstrut -\mathstrut 13860q^{29} \) \(\mathstrut -\mathstrut 11880q^{30} \) \(\mathstrut +\mathstrut 13504q^{31} \) \(\mathstrut +\mathstrut 9152q^{34} \) \(\mathstrut +\mathstrut 3960q^{35} \) \(\mathstrut +\mathstrut 3672q^{36} \) \(\mathstrut -\mathstrut 4752q^{39} \) \(\mathstrut -\mathstrut 8800q^{40} \) \(\mathstrut -\mathstrut 396q^{41} \) \(\mathstrut -\mathstrut 6048q^{44} \) \(\mathstrut +\mathstrut 13770q^{45} \) \(\mathstrut -\mathstrut 32296q^{46} \) \(\mathstrut +\mathstrut 26486q^{49} \) \(\mathstrut +\mathstrut 39600q^{50} \) \(\mathstrut -\mathstrut 27456q^{51} \) \(\mathstrut +\mathstrut 23760q^{54} \) \(\mathstrut -\mathstrut 22680q^{55} \) \(\mathstrut +\mathstrut 15840q^{56} \) \(\mathstrut -\mathstrut 49320q^{59} \) \(\mathstrut -\mathstrut 15840q^{60} \) \(\mathstrut -\mathstrut 11396q^{61} \) \(\mathstrut -\mathstrut 25984q^{64} \) \(\mathstrut +\mathstrut 7920q^{65} \) \(\mathstrut +\mathstrut 66528q^{66} \) \(\mathstrut +\mathstrut 96888q^{69} \) \(\mathstrut -\mathstrut 35640q^{70} \) \(\mathstrut +\mathstrut 106704q^{71} \) \(\mathstrut -\mathstrut 185328q^{74} \) \(\mathstrut -\mathstrut 118800q^{75} \) \(\mathstrut +\mathstrut 5280q^{76} \) \(\mathstrut +\mathstrut 103840q^{79} \) \(\mathstrut +\mathstrut 113760q^{80} \) \(\mathstrut -\mathstrut 145638q^{81} \) \(\mathstrut +\mathstrut 28512q^{84} \) \(\mathstrut +\mathstrut 45760q^{85} \) \(\mathstrut +\mathstrut 5544q^{86} \) \(\mathstrut -\mathstrut 19980q^{89} \) \(\mathstrut +\mathstrut 67320q^{90} \) \(\mathstrut -\mathstrut 14256q^{91} \) \(\mathstrut +\mathstrut 139832q^{94} \) \(\mathstrut +\mathstrut 19800q^{95} \) \(\mathstrut -\mathstrut 164736q^{96} \) \(\mathstrut -\mathstrut 77112q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(5, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.6.b.a \(2\) \(0.802\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-90\) \(0\) \(q-\beta q^{2}+3\beta q^{3}-12q^{4}+(-45-5\beta )q^{5}+\cdots\)