Properties

Label 20.3.d
Level 20
Weight 3
Character orbit d
Rep. character \(\chi_{20}(19,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 3
Sturm bound 9
Trace bound 2

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4q - 4q^{5} - 16q^{6} - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{5} - 16q^{6} - 4q^{9} + 16q^{10} + 16q^{14} + 64q^{16} - 64q^{20} - 32q^{21} - 64q^{24} + 36q^{25} - 96q^{26} + 40q^{29} + 80q^{30} + 64q^{34} + 128q^{36} - 64q^{40} + 88q^{41} - 124q^{45} - 176q^{46} - 164q^{49} + 96q^{50} + 32q^{54} + 64q^{56} - 72q^{61} + 192q^{65} + 352q^{69} - 80q^{70} - 96q^{74} - 64q^{80} - 28q^{81} - 128q^{84} - 128q^{85} + 304q^{86} - 440q^{89} - 144q^{90} + 16q^{94} - 256q^{96} + O(q^{100}) \)

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.d.a \(1\) \(0.545\) \(\Q\) \(\Q(\sqrt{-5}) \) \(-2\) \(4\) \(-5\) \(-4\) \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.b \(1\) \(0.545\) \(\Q\) \(\Q(\sqrt{-5}) \) \(2\) \(-4\) \(-5\) \(4\) \(q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.c \(2\) \(0.545\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) \(q+iq^{2}-4q^{4}+(3-2i)q^{5}-4iq^{8}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T \))(\( 1 - 2 T \))(\( 1 + 4 T^{2} \))
$3$ (\( 1 - 4 T + 9 T^{2} \))(\( 1 + 4 T + 9 T^{2} \))(\( ( 1 + 9 T^{2} )^{2} \))
$5$ (\( 1 + 5 T \))(\( 1 + 5 T \))(\( 1 - 6 T + 25 T^{2} \))
$7$ (\( 1 + 4 T + 49 T^{2} \))(\( 1 - 4 T + 49 T^{2} \))(\( ( 1 + 49 T^{2} )^{2} \))
$11$ (\( ( 1 - 11 T )( 1 + 11 T ) \))(\( ( 1 - 11 T )( 1 + 11 T ) \))(\( ( 1 - 11 T )^{2}( 1 + 11 T )^{2} \))
$13$ (\( ( 1 - 13 T )( 1 + 13 T ) \))(\( ( 1 - 13 T )( 1 + 13 T ) \))(\( ( 1 - 10 T + 169 T^{2} )( 1 + 10 T + 169 T^{2} ) \))
$17$ (\( ( 1 - 17 T )( 1 + 17 T ) \))(\( ( 1 - 17 T )( 1 + 17 T ) \))(\( ( 1 - 30 T + 289 T^{2} )( 1 + 30 T + 289 T^{2} ) \))
$19$ (\( ( 1 - 19 T )( 1 + 19 T ) \))(\( ( 1 - 19 T )( 1 + 19 T ) \))(\( ( 1 - 19 T )^{2}( 1 + 19 T )^{2} \))
$23$ (\( 1 - 44 T + 529 T^{2} \))(\( 1 + 44 T + 529 T^{2} \))(\( ( 1 + 529 T^{2} )^{2} \))
$29$ (\( 1 + 22 T + 841 T^{2} \))(\( 1 + 22 T + 841 T^{2} \))(\( ( 1 - 42 T + 841 T^{2} )^{2} \))
$31$ (\( ( 1 - 31 T )( 1 + 31 T ) \))(\( ( 1 - 31 T )( 1 + 31 T ) \))(\( ( 1 - 31 T )^{2}( 1 + 31 T )^{2} \))
$37$ (\( ( 1 - 37 T )( 1 + 37 T ) \))(\( ( 1 - 37 T )( 1 + 37 T ) \))(\( ( 1 - 70 T + 1369 T^{2} )( 1 + 70 T + 1369 T^{2} ) \))
$41$ (\( 1 - 62 T + 1681 T^{2} \))(\( 1 - 62 T + 1681 T^{2} \))(\( ( 1 + 18 T + 1681 T^{2} )^{2} \))
$43$ (\( 1 + 76 T + 1849 T^{2} \))(\( 1 - 76 T + 1849 T^{2} \))(\( ( 1 + 1849 T^{2} )^{2} \))
$47$ (\( 1 + 4 T + 2209 T^{2} \))(\( 1 - 4 T + 2209 T^{2} \))(\( ( 1 + 2209 T^{2} )^{2} \))
$53$ (\( ( 1 - 53 T )( 1 + 53 T ) \))(\( ( 1 - 53 T )( 1 + 53 T ) \))(\( ( 1 - 90 T + 2809 T^{2} )( 1 + 90 T + 2809 T^{2} ) \))
$59$ (\( ( 1 - 59 T )( 1 + 59 T ) \))(\( ( 1 - 59 T )( 1 + 59 T ) \))(\( ( 1 - 59 T )^{2}( 1 + 59 T )^{2} \))
$61$ (\( 1 + 58 T + 3721 T^{2} \))(\( 1 + 58 T + 3721 T^{2} \))(\( ( 1 - 22 T + 3721 T^{2} )^{2} \))
$67$ (\( 1 - 116 T + 4489 T^{2} \))(\( 1 + 116 T + 4489 T^{2} \))(\( ( 1 + 4489 T^{2} )^{2} \))
$71$ (\( ( 1 - 71 T )( 1 + 71 T ) \))(\( ( 1 - 71 T )( 1 + 71 T ) \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))
$73$ (\( ( 1 - 73 T )( 1 + 73 T ) \))(\( ( 1 - 73 T )( 1 + 73 T ) \))(\( ( 1 - 110 T + 5329 T^{2} )( 1 + 110 T + 5329 T^{2} ) \))
$79$ (\( ( 1 - 79 T )( 1 + 79 T ) \))(\( ( 1 - 79 T )( 1 + 79 T ) \))(\( ( 1 - 79 T )^{2}( 1 + 79 T )^{2} \))
$83$ (\( 1 + 76 T + 6889 T^{2} \))(\( 1 - 76 T + 6889 T^{2} \))(\( ( 1 + 6889 T^{2} )^{2} \))
$89$ (\( 1 + 142 T + 7921 T^{2} \))(\( 1 + 142 T + 7921 T^{2} \))(\( ( 1 + 78 T + 7921 T^{2} )^{2} \))
$97$ (\( ( 1 - 97 T )( 1 + 97 T ) \))(\( ( 1 - 97 T )( 1 + 97 T ) \))(\( ( 1 - 130 T + 9409 T^{2} )( 1 + 130 T + 9409 T^{2} ) \))
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