Properties

Label 10.6.b
Level 10
Weight 6
Character orbit b
Rep. character \(\chi_{10}(9,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 10.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(10, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 6 2 4
Eisenstein series 4 0 4

Trace form

\(2q \) \(\mathstrut -\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 110q^{5} \) \(\mathstrut -\mathstrut 112q^{6} \) \(\mathstrut +\mathstrut 94q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 110q^{5} \) \(\mathstrut -\mathstrut 112q^{6} \) \(\mathstrut +\mathstrut 94q^{9} \) \(\mathstrut -\mathstrut 80q^{10} \) \(\mathstrut -\mathstrut 296q^{11} \) \(\mathstrut +\mathstrut 1264q^{14} \) \(\mathstrut -\mathstrut 280q^{15} \) \(\mathstrut +\mathstrut 512q^{16} \) \(\mathstrut -\mathstrut 4440q^{19} \) \(\mathstrut -\mathstrut 1760q^{20} \) \(\mathstrut +\mathstrut 4424q^{21} \) \(\mathstrut +\mathstrut 1792q^{24} \) \(\mathstrut +\mathstrut 5850q^{25} \) \(\mathstrut -\mathstrut 5472q^{26} \) \(\mathstrut +\mathstrut 540q^{29} \) \(\mathstrut -\mathstrut 6160q^{30} \) \(\mathstrut -\mathstrut 4096q^{31} \) \(\mathstrut +\mathstrut 16384q^{34} \) \(\mathstrut +\mathstrut 3160q^{35} \) \(\mathstrut -\mathstrut 1504q^{36} \) \(\mathstrut -\mathstrut 19152q^{39} \) \(\mathstrut +\mathstrut 1280q^{40} \) \(\mathstrut -\mathstrut 4796q^{41} \) \(\mathstrut +\mathstrut 4736q^{44} \) \(\mathstrut +\mathstrut 5170q^{45} \) \(\mathstrut +\mathstrut 9968q^{46} \) \(\mathstrut -\mathstrut 16314q^{49} \) \(\mathstrut -\mathstrut 8800q^{50} \) \(\mathstrut +\mathstrut 57344q^{51} \) \(\mathstrut -\mathstrut 32480q^{54} \) \(\mathstrut -\mathstrut 16280q^{55} \) \(\mathstrut -\mathstrut 20224q^{56} \) \(\mathstrut +\mathstrut 79480q^{59} \) \(\mathstrut +\mathstrut 4480q^{60} \) \(\mathstrut -\mathstrut 84596q^{61} \) \(\mathstrut -\mathstrut 8192q^{64} \) \(\mathstrut -\mathstrut 13680q^{65} \) \(\mathstrut +\mathstrut 16576q^{66} \) \(\mathstrut +\mathstrut 34888q^{69} \) \(\mathstrut +\mathstrut 69520q^{70} \) \(\mathstrut -\mathstrut 8496q^{71} \) \(\mathstrut -\mathstrut 34976q^{74} \) \(\mathstrut -\mathstrut 30800q^{75} \) \(\mathstrut +\mathstrut 71040q^{76} \) \(\mathstrut -\mathstrut 70560q^{79} \) \(\mathstrut +\mathstrut 28160q^{80} \) \(\mathstrut -\mathstrut 90838q^{81} \) \(\mathstrut -\mathstrut 70784q^{84} \) \(\mathstrut +\mathstrut 40960q^{85} \) \(\mathstrut -\mathstrut 18352q^{86} \) \(\mathstrut +\mathstrut 170420q^{89} \) \(\mathstrut -\mathstrut 3760q^{90} \) \(\mathstrut +\mathstrut 216144q^{91} \) \(\mathstrut -\mathstrut 85456q^{94} \) \(\mathstrut -\mathstrut 244200q^{95} \) \(\mathstrut -\mathstrut 28672q^{96} \) \(\mathstrut -\mathstrut 13912q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(10, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
10.6.b.a \(2\) \(1.604\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(110\) \(0\) \(q+2iq^{2}+7iq^{3}-2^{4}q^{4}+(55+5i)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)