Properties

Label 920.2.bb
Level $920$
Weight $2$
Character orbit 920.bb
Rep. character $\chi_{920}(11,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $960$
Newform subspaces $2$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bb (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 1480 960 520
Cusp forms 1400 960 440
Eisenstein series 80 0 80

Trace form

\( 960q + 4q^{2} - 8q^{4} + 10q^{6} - 2q^{8} - 96q^{9} + O(q^{10}) \) \( 960q + 4q^{2} - 8q^{4} + 10q^{6} - 2q^{8} - 96q^{9} + 6q^{12} - 24q^{16} + 14q^{18} + 4q^{24} - 96q^{25} + 14q^{26} + 24q^{27} - 16q^{32} - 22q^{34} + 108q^{36} - 110q^{38} + 88q^{40} + 22q^{44} - 152q^{46} + 110q^{48} - 96q^{49} - 18q^{50} - 14q^{52} - 54q^{54} + 110q^{56} - 80q^{58} - 24q^{59} + 22q^{60} + 30q^{62} - 14q^{64} + 6q^{72} - 22q^{74} - 182q^{78} - 112q^{81} - 118q^{82} - 308q^{84} - 176q^{88} - 130q^{92} - 148q^{94} + 130q^{96} - 196q^{98} + O(q^{100}) \)

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.bb.a \(480\) \(7.346\) None \(2\) \(0\) \(-48\) \(0\)
920.2.bb.b \(480\) \(7.346\) None \(2\) \(0\) \(48\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)