Properties

Label 920.2.bf
Level $920$
Weight $2$
Character orbit 920.bf
Rep. character $\chi_{920}(29,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1400$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bf (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 920 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(920, [\chi])\).

Total New Old
Modular forms 1480 1480 0
Cusp forms 1400 1400 0
Eisenstein series 80 80 0

Trace form

\( 1400q - 14q^{4} - 14q^{6} - 168q^{9} + O(q^{10}) \) \( 1400q - 14q^{4} - 14q^{6} - 168q^{9} - 5q^{10} - 26q^{14} - 6q^{15} - 14q^{16} - 27q^{20} - 32q^{24} - 18q^{25} - 30q^{26} - q^{30} - 52q^{31} + 40q^{34} + 26q^{36} - 12q^{39} + 15q^{40} - 36q^{41} - 142q^{44} - 10q^{46} + 80q^{49} - 47q^{50} + 46q^{54} - 38q^{55} + 14q^{56} + 21q^{60} - 26q^{64} + 2q^{65} - 104q^{66} - 26q^{70} - 36q^{71} - 18q^{74} - 96q^{76} - 12q^{79} + 82q^{80} - 136q^{81} - 82q^{84} - 198q^{86} - 52q^{89} + 164q^{90} - 38q^{94} + 2q^{95} - 432q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(920, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
920.2.bf.a \(1400\) \(7.346\) None \(0\) \(0\) \(0\) \(0\)