Properties

Label 20.3.f
Level 20
Weight 3
Character orbit f
Rep. character \(\chi_{20}(13,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 2
Newform subspaces 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 20.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(20, [\chi])\).

Total New Old
Modular forms 18 2 16
Cusp forms 6 2 4
Eisenstein series 12 0 12

Trace form

\( 2q + 2q^{3} - 6q^{5} - 14q^{7} + O(q^{10}) \) \( 2q + 2q^{3} - 6q^{5} - 14q^{7} + 20q^{11} + 18q^{13} + 2q^{15} + 2q^{17} - 28q^{21} - 46q^{23} - 14q^{25} + 32q^{27} - 28q^{31} + 20q^{33} + 98q^{35} + 66q^{37} - 28q^{41} - 30q^{43} - 56q^{45} - 78q^{47} + 4q^{51} - 14q^{53} - 60q^{55} - 16q^{57} + 84q^{61} + 98q^{63} + 18q^{65} - 14q^{67} + 196q^{71} + 98q^{73} - 62q^{75} - 140q^{77} - 62q^{81} - 126q^{83} - 14q^{85} - 16q^{87} - 252q^{91} - 28q^{93} + 64q^{95} + 66q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.3.f.a \(2\) \(0.545\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-6\) \(-14\) \(q+(1-i)q^{3}+(-3+4i)q^{5}+(-7-7i)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 2 T + 2 T^{2} - 18 T^{3} + 81 T^{4} \)
$5$ \( 1 + 6 T + 25 T^{2} \)
$7$ \( ( 1 + 7 T )^{2}( 1 + 49 T^{2} ) \)
$11$ \( ( 1 - 10 T + 121 T^{2} )^{2} \)
$13$ \( 1 - 18 T + 162 T^{2} - 3042 T^{3} + 28561 T^{4} \)
$17$ \( 1 - 2 T + 2 T^{2} - 578 T^{3} + 83521 T^{4} \)
$19$ \( 1 - 658 T^{2} + 130321 T^{4} \)
$23$ \( ( 1 + 23 T )^{2}( 1 + 529 T^{2} ) \)
$29$ \( 1 - 1618 T^{2} + 707281 T^{4} \)
$31$ \( ( 1 + 14 T + 961 T^{2} )^{2} \)
$37$ \( 1 - 66 T + 2178 T^{2} - 90354 T^{3} + 1874161 T^{4} \)
$41$ \( ( 1 + 14 T + 1681 T^{2} )^{2} \)
$43$ \( 1 + 30 T + 450 T^{2} + 55470 T^{3} + 3418801 T^{4} \)
$47$ \( 1 + 78 T + 3042 T^{2} + 172302 T^{3} + 4879681 T^{4} \)
$53$ \( 1 + 14 T + 98 T^{2} + 39326 T^{3} + 7890481 T^{4} \)
$59$ \( 1 - 3826 T^{2} + 12117361 T^{4} \)
$61$ \( ( 1 - 42 T + 3721 T^{2} )^{2} \)
$67$ \( 1 + 14 T + 98 T^{2} + 62846 T^{3} + 20151121 T^{4} \)
$71$ \( ( 1 - 98 T + 5041 T^{2} )^{2} \)
$73$ \( 1 - 98 T + 4802 T^{2} - 522242 T^{3} + 28398241 T^{4} \)
$79$ \( 1 - 3266 T^{2} + 38950081 T^{4} \)
$83$ \( 1 + 126 T + 7938 T^{2} + 868014 T^{3} + 47458321 T^{4} \)
$89$ \( 1 - 3298 T^{2} + 62742241 T^{4} \)
$97$ \( 1 - 66 T + 2178 T^{2} - 620994 T^{3} + 88529281 T^{4} \)
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