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Properties

Label 920.2.x
Level $920$
Weight $2$
Character orbit 920.x
Rep. character $\chi_{920}(413,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $280$
Newform subspaces $3$
Sturm bound $288$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 920 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(288\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

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

Total New Old
Modular forms 296 296 0
Cusp forms 280 280 0
Eisenstein series 16 16 0

Trace form

\( 280 q - 4 q^{2} - 16 q^{6} - 4 q^{8} + O(q^{10}) \) \( 280 q - 4 q^{2} - 16 q^{6} - 4 q^{8} - 16 q^{12} + 16 q^{18} - 4 q^{23} - 8 q^{25} - 8 q^{26} + 16 q^{31} + 16 q^{32} - 8 q^{36} - 16 q^{41} - 16 q^{46} - 8 q^{47} - 12 q^{48} - 20 q^{50} - 96 q^{52} - 48 q^{55} + 20 q^{58} - 68 q^{62} + 20 q^{70} - 16 q^{71} + 16 q^{72} - 8 q^{73} + 92 q^{78} - 264 q^{81} - 12 q^{82} - 32 q^{87} - 20 q^{92} + 32 q^{95} + 80 q^{96} - 52 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.x.a 920.x 920.x $8$ $7.346$ 8.0.\(\cdots\).4 \(\Q(\sqrt{-46}) \) \(-8\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+\beta _{4})q^{2}-2\beta _{4}q^{4}+\beta _{1}q^{5}+\cdots\)
920.2.x.b 920.x 920.x $8$ $7.346$ 8.0.\(\cdots\).4 \(\Q(\sqrt{-46}) \) \(8\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-\beta _{3})q^{2}-2\beta _{3}q^{4}-\beta _{4}q^{5}+(-2+\cdots)q^{8}+\cdots\)
920.2.x.c 920.x 920.x $264$ $7.346$ None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$