Properties

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(20))\).

Total New Old
Modular forms 12 1 11
Cusp forms 6 1 5
Eisenstein series 6 0 6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)FrickeDim.
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\( q + 4q^{3} + 5q^{5} - 16q^{7} - 11q^{9} + O(q^{10}) \) \( q + 4q^{3} + 5q^{5} - 16q^{7} - 11q^{9} - 60q^{11} + 86q^{13} + 20q^{15} + 18q^{17} + 44q^{19} - 64q^{21} + 48q^{23} + 25q^{25} - 152q^{27} - 186q^{29} + 176q^{31} - 240q^{33} - 80q^{35} + 254q^{37} + 344q^{39} + 186q^{41} - 100q^{43} - 55q^{45} + 168q^{47} - 87q^{49} + 72q^{51} - 498q^{53} - 300q^{55} + 176q^{57} - 252q^{59} - 58q^{61} + 176q^{63} + 430q^{65} - 1036q^{67} + 192q^{69} + 168q^{71} + 506q^{73} + 100q^{75} + 960q^{77} + 272q^{79} - 311q^{81} + 948q^{83} + 90q^{85} - 744q^{87} - 1014q^{89} - 1376q^{91} + 704q^{93} + 220q^{95} - 766q^{97} + 660q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(20))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
20.4.a.a \(1\) \(1.180\) \(\Q\) None \(0\) \(4\) \(5\) \(-16\) \(-\) \(-\) \(q+4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(20)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 4 T + 27 T^{2} \)
$5$ \( 1 - 5 T \)
$7$ \( 1 + 16 T + 343 T^{2} \)
$11$ \( 1 + 60 T + 1331 T^{2} \)
$13$ \( 1 - 86 T + 2197 T^{2} \)
$17$ \( 1 - 18 T + 4913 T^{2} \)
$19$ \( 1 - 44 T + 6859 T^{2} \)
$23$ \( 1 - 48 T + 12167 T^{2} \)
$29$ \( 1 + 186 T + 24389 T^{2} \)
$31$ \( 1 - 176 T + 29791 T^{2} \)
$37$ \( 1 - 254 T + 50653 T^{2} \)
$41$ \( 1 - 186 T + 68921 T^{2} \)
$43$ \( 1 + 100 T + 79507 T^{2} \)
$47$ \( 1 - 168 T + 103823 T^{2} \)
$53$ \( 1 + 498 T + 148877 T^{2} \)
$59$ \( 1 + 252 T + 205379 T^{2} \)
$61$ \( 1 + 58 T + 226981 T^{2} \)
$67$ \( 1 + 1036 T + 300763 T^{2} \)
$71$ \( 1 - 168 T + 357911 T^{2} \)
$73$ \( 1 - 506 T + 389017 T^{2} \)
$79$ \( 1 - 272 T + 493039 T^{2} \)
$83$ \( 1 - 948 T + 571787 T^{2} \)
$89$ \( 1 + 1014 T + 704969 T^{2} \)
$97$ \( 1 + 766 T + 912673 T^{2} \)
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