Properties

Label 20.2.e
Level 20
Weight 2
Character orbit e
Rep. character \(\chi_{20}(3,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 2
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 20.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(20, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 2 2 0
Eisenstein series 8 8 0

Trace form

\( 2q - 2q^{2} - 4q^{5} + 4q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{5} + 4q^{8} + 6q^{10} - 2q^{13} - 8q^{16} + 6q^{17} - 6q^{18} - 4q^{20} + 6q^{25} + 4q^{26} + 8q^{32} + 12q^{36} - 14q^{37} - 4q^{40} - 16q^{41} + 6q^{45} - 14q^{50} - 4q^{52} + 18q^{53} + 8q^{58} + 24q^{61} + 2q^{65} - 12q^{68} - 12q^{72} - 22q^{73} + 16q^{80} - 18q^{81} + 16q^{82} - 18q^{85} + 6q^{90} + 26q^{97} + 14q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.2.e.a \(2\) \(0.160\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(-4\) \(0\) \(q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T + 2 T^{2} \)
$3$ \( 1 + 9 T^{4} \)
$5$ \( 1 + 4 T + 5 T^{2} \)
$7$ \( 1 + 49 T^{4} \)
$11$ \( ( 1 - 11 T^{2} )^{2} \)
$13$ \( ( 1 - 4 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \)
$17$ \( ( 1 - 8 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} ) \)
$19$ \( ( 1 + 19 T^{2} )^{2} \)
$23$ \( 1 + 529 T^{4} \)
$29$ \( ( 1 - 10 T + 29 T^{2} )( 1 + 10 T + 29 T^{2} ) \)
$31$ \( ( 1 - 31 T^{2} )^{2} \)
$37$ \( ( 1 + 2 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \)
$41$ \( ( 1 + 8 T + 41 T^{2} )^{2} \)
$43$ \( 1 + 1849 T^{4} \)
$47$ \( 1 + 2209 T^{4} \)
$53$ \( ( 1 - 14 T + 53 T^{2} )( 1 - 4 T + 53 T^{2} ) \)
$59$ \( ( 1 + 59 T^{2} )^{2} \)
$61$ \( ( 1 - 12 T + 61 T^{2} )^{2} \)
$67$ \( 1 + 4489 T^{4} \)
$71$ \( ( 1 - 71 T^{2} )^{2} \)
$73$ \( ( 1 + 6 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \)
$79$ \( ( 1 + 79 T^{2} )^{2} \)
$83$ \( 1 + 6889 T^{4} \)
$89$ \( ( 1 - 10 T + 89 T^{2} )( 1 + 10 T + 89 T^{2} ) \)
$97$ \( ( 1 - 18 T + 97 T^{2} )( 1 - 8 T + 97 T^{2} ) \)
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