Properties

Label 920.2.bo
Level $920$
Weight $2$
Character orbit 920.bo
Rep. character $\chi_{920}(37,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $2800$
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.bo (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 920 \)
Character field: \(\Q(\zeta_{44})\)
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 2960 2960 0
Cusp forms 2800 2800 0
Eisenstein series 160 160 0

Trace form

\( 2800q - 18q^{2} - 28q^{6} - 44q^{7} - 18q^{8} + O(q^{10}) \) \( 2800q - 18q^{2} - 28q^{6} - 44q^{7} - 18q^{8} - 22q^{10} - 6q^{12} - 44q^{15} - 44q^{16} - 44q^{17} - 38q^{18} - 22q^{20} - 40q^{23} - 36q^{25} - 36q^{26} - 22q^{28} - 22q^{30} - 104q^{31} - 38q^{32} - 44q^{33} - 36q^{36} - 22q^{38} - 22q^{40} - 72q^{41} + 198q^{42} - 28q^{46} - 80q^{47} - 10q^{48} - 2q^{50} - 146q^{52} + 4q^{55} - 44q^{56} - 44q^{57} - 42q^{58} - 22q^{60} + 46q^{62} - 44q^{63} - 44q^{65} - 44q^{66} - 64q^{70} - 72q^{71} - 104q^{72} - 36q^{73} - 44q^{76} - 114q^{78} - 220q^{80} + 176q^{81} - 10q^{82} - 44q^{86} - 12q^{87} - 22q^{88} - 440q^{90} - 2q^{92} - 76q^{95} - 124q^{96} - 44q^{97} + 30q^{98} + O(q^{100}) \)

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.bo.a \(2800\) \(7.346\) None \(-18\) \(0\) \(0\) \(-44\)