Properties

Label 920.2.b
Level $920$
Weight $2$
Character orbit 920.b
Rep. character $\chi_{920}(459,\cdot)$
Character field $\Q$
Dimension $140$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 920 \)
Character field: \(\Q\)
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 148 148 0
Cusp forms 140 140 0
Eisenstein series 8 8 0

Trace form

\( 140q + 8q^{6} - 140q^{9} + O(q^{10}) \) \( 140q + 8q^{6} - 140q^{9} - 8q^{16} + 4q^{24} - 4q^{25} + 8q^{26} + 16q^{35} - 24q^{36} - 8q^{41} - 8q^{46} - 124q^{49} + 4q^{50} - 76q^{54} - 8q^{59} + 36q^{64} - 8q^{70} + 8q^{75} + 108q^{81} + 44q^{94} + 16q^{96} + O(q^{100}) \)

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.b.a \(4\) \(7.346\) \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+2q^{4}-\beta _{3}q^{5}-2\beta _{3}q^{7}+\cdots\)
920.2.b.b \(136\) \(7.346\) None \(0\) \(0\) \(0\) \(0\)