Properties

Label 920.2.bn
Level $920$
Weight $2$
Character orbit 920.bn
Rep. character $\chi_{920}(19,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1400$
Newform subspaces $2$
Sturm bound $288$
Trace bound $1$

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Defining parameters

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

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

\( 1400q - 22q^{4} - 30q^{6} + 96q^{9} + O(q^{10}) \) \( 1400q - 22q^{4} - 30q^{6} + 96q^{9} - 11q^{10} - 44q^{11} - 22q^{14} - 14q^{16} - 44q^{19} - 11q^{20} - 48q^{24} - 18q^{25} - 30q^{26} - 11q^{30} - 44q^{34} - 38q^{35} + 2q^{36} - 11q^{40} - 36q^{41} + 110q^{44} - 14q^{46} + 80q^{49} - 15q^{50} - 44q^{51} - 34q^{54} - 22q^{56} - 36q^{59} - 11q^{60} - 58q^{64} - 22q^{65} - 88q^{66} - 14q^{70} - 22q^{74} - 30q^{75} - 132q^{76} + 88q^{80} - 152q^{81} - 22q^{84} - 242q^{86} - 44q^{89} + 220q^{90} - 110q^{94} - 456q^{96} - 44q^{99} + O(q^{100}) \)

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.bn.a \(40\) \(7.346\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\)
920.2.bn.b \(1360\) \(7.346\) None \(0\) \(0\) \(0\) \(0\)