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 $0$

Related objects

Downloads

Learn more

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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
920.2.bo.a 920.bo 920.ao $2800$ $7.346$ None \(-18\) \(0\) \(0\) \(-44\) $\mathrm{SU}(2)[C_{44}]$