Properties

Label 10.4.b
Level 10
Weight 4
Character orbit b
Rep. character \(\chi_{10}(9,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 10.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(10, [\chi])\).

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

Trace form

\(2q \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut 40q^{10} \) \(\mathstrut -\mathstrut 56q^{11} \) \(\mathstrut -\mathstrut 104q^{14} \) \(\mathstrut -\mathstrut 40q^{15} \) \(\mathstrut +\mathstrut 32q^{16} \) \(\mathstrut +\mathstrut 120q^{19} \) \(\mathstrut +\mathstrut 40q^{20} \) \(\mathstrut +\mathstrut 104q^{21} \) \(\mathstrut -\mathstrut 32q^{24} \) \(\mathstrut -\mathstrut 150q^{25} \) \(\mathstrut +\mathstrut 48q^{26} \) \(\mathstrut -\mathstrut 180q^{29} \) \(\mathstrut -\mathstrut 40q^{30} \) \(\mathstrut -\mathstrut 256q^{31} \) \(\mathstrut +\mathstrut 256q^{34} \) \(\mathstrut +\mathstrut 520q^{35} \) \(\mathstrut -\mathstrut 184q^{36} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 160q^{40} \) \(\mathstrut +\mathstrut 484q^{41} \) \(\mathstrut +\mathstrut 224q^{44} \) \(\mathstrut -\mathstrut 230q^{45} \) \(\mathstrut -\mathstrut 232q^{46} \) \(\mathstrut -\mathstrut 666q^{49} \) \(\mathstrut -\mathstrut 400q^{50} \) \(\mathstrut -\mathstrut 256q^{51} \) \(\mathstrut +\mathstrut 400q^{54} \) \(\mathstrut +\mathstrut 280q^{55} \) \(\mathstrut +\mathstrut 416q^{56} \) \(\mathstrut +\mathstrut 40q^{59} \) \(\mathstrut +\mathstrut 160q^{60} \) \(\mathstrut +\mathstrut 1084q^{61} \) \(\mathstrut -\mathstrut 128q^{64} \) \(\mathstrut -\mathstrut 240q^{65} \) \(\mathstrut -\mathstrut 224q^{66} \) \(\mathstrut +\mathstrut 232q^{69} \) \(\mathstrut +\mathstrut 520q^{70} \) \(\mathstrut -\mathstrut 2256q^{71} \) \(\mathstrut -\mathstrut 944q^{74} \) \(\mathstrut +\mathstrut 400q^{75} \) \(\mathstrut -\mathstrut 480q^{76} \) \(\mathstrut +\mathstrut 1440q^{79} \) \(\mathstrut -\mathstrut 160q^{80} \) \(\mathstrut +\mathstrut 842q^{81} \) \(\mathstrut -\mathstrut 416q^{84} \) \(\mathstrut -\mathstrut 1280q^{85} \) \(\mathstrut +\mathstrut 1448q^{86} \) \(\mathstrut +\mathstrut 980q^{89} \) \(\mathstrut +\mathstrut 920q^{90} \) \(\mathstrut +\mathstrut 624q^{91} \) \(\mathstrut -\mathstrut 904q^{94} \) \(\mathstrut -\mathstrut 600q^{95} \) \(\mathstrut +\mathstrut 128q^{96} \) \(\mathstrut -\mathstrut 1288q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(10, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
10.4.b.a \(2\) \(0.590\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-10\) \(0\) \(q+iq^{2}-iq^{3}-4q^{4}+(-5-5i)q^{5}+\cdots\)