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Properties

Label 2020.1.bc
Level $2020$
Weight $1$
Character orbit 2020.bc
Rep. character $\chi_{2020}(163,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $8$
Newform subspaces $1$
Sturm bound $306$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2020 = 2^{2} \cdot 5 \cdot 101 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2020.bc (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2020 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(306\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2020, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 8 8 0
Eisenstein series 32 32 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{8} + 2 q^{9} + O(q^{10}) \) \( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{8} + 2 q^{9} - 8 q^{13} - 2 q^{16} - 8 q^{17} - 2 q^{18} + 2 q^{25} - 2 q^{26} + 2 q^{29} - 8 q^{32} - 2 q^{34} - 8 q^{36} + 2 q^{37} + 2 q^{41} - 2 q^{49} + 8 q^{50} + 2 q^{52} - 2 q^{58} - 2 q^{61} - 2 q^{64} + 2 q^{65} + 2 q^{68} - 2 q^{72} + 8 q^{74} - 2 q^{81} - 2 q^{82} - 2 q^{85} + 2 q^{89} + 2 q^{97} + 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2020, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2020.1.bc.a 2020.bc 2020.ac $8$ $1.008$ \(\Q(\zeta_{20})\) $D_{20}$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{6}q^{2}-\zeta_{20}^{2}q^{4}+\zeta_{20}^{7}q^{5}+\cdots\)