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

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

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.x.a \(8\) \(7.346\) 8.0.\(\cdots\).4 \(\Q(\sqrt{-46}) \) \(-8\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{4})q^{2}-2\beta _{4}q^{4}+\beta _{1}q^{5}+\cdots\)
920.2.x.b \(8\) \(7.346\) 8.0.\(\cdots\).4 \(\Q(\sqrt{-46}) \) \(8\) \(0\) \(0\) \(0\) \(q+(1-\beta _{3})q^{2}-2\beta _{3}q^{4}-\beta _{4}q^{5}+(-2+\cdots)q^{8}+\cdots\)
920.2.x.c \(264\) \(7.346\) None \(-4\) \(0\) \(0\) \(0\)