Properties

Label 20.4.c
Level 20
Weight 4
Character orbit c
Rep. character \(\chi_{20}(9,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 20.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(20, [\chi])\).

Total New Old
Modular forms 12 2 10
Cusp forms 6 2 4
Eisenstein series 6 0 6

Trace form

\( 2q + 14q^{5} - 98q^{9} + O(q^{10}) \) \( 2q + 14q^{5} - 98q^{9} + 40q^{11} + 152q^{15} - 168q^{19} + 152q^{21} - 54q^{25} + 12q^{29} - 448q^{31} - 152q^{35} + 912q^{39} + 532q^{41} - 686q^{45} + 534q^{49} - 1216q^{51} + 280q^{55} - 56q^{59} + 364q^{61} - 912q^{65} - 1064q^{69} + 816q^{71} + 2128q^{75} + 96q^{79} + 698q^{81} + 1216q^{85} - 3052q^{89} - 912q^{91} - 1176q^{95} - 1960q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.4.c.a \(2\) \(1.180\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(14\) \(0\) \(q-\beta q^{3}+(7+\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 + 22 T^{2} + 729 T^{4} \)
$5$ \( 1 - 14 T + 125 T^{2} \)
$7$ \( ( 1 - 36 T + 343 T^{2} )( 1 + 36 T + 343 T^{2} ) \)
$11$ \( ( 1 - 20 T + 1331 T^{2} )^{2} \)
$13$ \( 1 - 1658 T^{2} + 4826809 T^{4} \)
$17$ \( 1 - 4962 T^{2} + 24137569 T^{4} \)
$19$ \( ( 1 + 84 T + 6859 T^{2} )^{2} \)
$23$ \( ( 1 - 212 T + 12167 T^{2} )( 1 + 212 T + 12167 T^{2} ) \)
$29$ \( ( 1 - 6 T + 24389 T^{2} )^{2} \)
$31$ \( ( 1 + 224 T + 29791 T^{2} )^{2} \)
$37$ \( 1 - 86410 T^{2} + 2565726409 T^{4} \)
$41$ \( ( 1 - 266 T + 68921 T^{2} )^{2} \)
$43$ \( 1 - 65914 T^{2} + 6321363049 T^{4} \)
$47$ \( 1 - 67122 T^{2} + 10779215329 T^{4} \)
$53$ \( 1 - 163690 T^{2} + 22164361129 T^{4} \)
$59$ \( ( 1 + 28 T + 205379 T^{2} )^{2} \)
$61$ \( ( 1 - 182 T + 226981 T^{2} )^{2} \)
$67$ \( 1 - 419050 T^{2} + 90458382169 T^{4} \)
$71$ \( ( 1 - 408 T + 357911 T^{2} )^{2} \)
$73$ \( 1 + 390542 T^{2} + 151334226289 T^{4} \)
$79$ \( ( 1 - 48 T + 493039 T^{2} )^{2} \)
$83$ \( 1 - 1103370 T^{2} + 326940373369 T^{4} \)
$89$ \( ( 1 + 1526 T + 704969 T^{2} )^{2} \)
$97$ \( 1 - 1514050 T^{2} + 832972004929 T^{4} \)
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