Properties

Label 10.4.b
Level $10$
Weight $4$
Character orbit 10.b
Rep. character $\chi_{10}(9,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

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 \(0\) \(0\) \(-10\) \(0\) \(q+iq^{2}-iq^{3}-4q^{4}+(-5-5i)q^{5}+\cdots\)