Properties

Label 6.5.b
Level 6
Weight 5
Character orbit b
Rep. character \(\chi_{6}(5,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\(2q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 48q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut -\mathstrut 126q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 48q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut -\mathstrut 126q^{9} \) \(\mathstrut -\mathstrut 96q^{10} \) \(\mathstrut +\mathstrut 48q^{12} \) \(\mathstrut +\mathstrut 100q^{13} \) \(\mathstrut +\mathstrut 288q^{15} \) \(\mathstrut +\mathstrut 128q^{16} \) \(\mathstrut -\mathstrut 288q^{18} \) \(\mathstrut -\mathstrut 716q^{19} \) \(\mathstrut -\mathstrut 156q^{21} \) \(\mathstrut +\mathstrut 672q^{22} \) \(\mathstrut -\mathstrut 384q^{24} \) \(\mathstrut +\mathstrut 674q^{25} \) \(\mathstrut +\mathstrut 1242q^{27} \) \(\mathstrut -\mathstrut 416q^{28} \) \(\mathstrut +\mathstrut 288q^{30} \) \(\mathstrut -\mathstrut 1484q^{31} \) \(\mathstrut -\mathstrut 2016q^{33} \) \(\mathstrut -\mathstrut 1152q^{34} \) \(\mathstrut +\mathstrut 1008q^{36} \) \(\mathstrut +\mathstrut 3748q^{37} \) \(\mathstrut -\mathstrut 300q^{39} \) \(\mathstrut +\mathstrut 768q^{40} \) \(\mathstrut +\mathstrut 1248q^{42} \) \(\mathstrut -\mathstrut 524q^{43} \) \(\mathstrut -\mathstrut 1728q^{45} \) \(\mathstrut -\mathstrut 2112q^{46} \) \(\mathstrut -\mathstrut 384q^{48} \) \(\mathstrut -\mathstrut 3450q^{49} \) \(\mathstrut +\mathstrut 3456q^{51} \) \(\mathstrut -\mathstrut 800q^{52} \) \(\mathstrut -\mathstrut 2160q^{54} \) \(\mathstrut +\mathstrut 4032q^{55} \) \(\mathstrut +\mathstrut 2148q^{57} \) \(\mathstrut +\mathstrut 8160q^{58} \) \(\mathstrut -\mathstrut 2304q^{60} \) \(\mathstrut -\mathstrut 2972q^{61} \) \(\mathstrut -\mathstrut 3276q^{63} \) \(\mathstrut -\mathstrut 1024q^{64} \) \(\mathstrut -\mathstrut 2016q^{66} \) \(\mathstrut -\mathstrut 8972q^{67} \) \(\mathstrut +\mathstrut 6336q^{69} \) \(\mathstrut -\mathstrut 2496q^{70} \) \(\mathstrut +\mathstrut 2304q^{72} \) \(\mathstrut +\mathstrut 580q^{73} \) \(\mathstrut -\mathstrut 2022q^{75} \) \(\mathstrut +\mathstrut 5728q^{76} \) \(\mathstrut +\mathstrut 2400q^{78} \) \(\mathstrut +\mathstrut 19636q^{79} \) \(\mathstrut +\mathstrut 2754q^{81} \) \(\mathstrut -\mathstrut 13632q^{82} \) \(\mathstrut +\mathstrut 1248q^{84} \) \(\mathstrut -\mathstrut 6912q^{85} \) \(\mathstrut -\mathstrut 24480q^{87} \) \(\mathstrut -\mathstrut 5376q^{88} \) \(\mathstrut +\mathstrut 6048q^{90} \) \(\mathstrut +\mathstrut 2600q^{91} \) \(\mathstrut +\mathstrut 4452q^{93} \) \(\mathstrut +\mathstrut 9600q^{94} \) \(\mathstrut +\mathstrut 3072q^{96} \) \(\mathstrut -\mathstrut 956q^{97} \) \(\mathstrut +\mathstrut 12096q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
6.5.b.a \(2\) \(0.620\) \(\Q(\sqrt{-2}) \) None \(0\) \(-6\) \(0\) \(52\) \(q+\beta q^{2}+(-3-3\beta )q^{3}-8q^{4}+6\beta q^{5}+\cdots\)