Properties

Label 20.6.a
Level 20
Weight 6
Character orbit a
Rep. character \(\chi_{20}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 20.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(20))\).

Total New Old
Modular forms 18 1 17
Cusp forms 12 1 11
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\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q + 22q^{3} - 25q^{5} + 218q^{7} + 241q^{9} + O(q^{10}) \) \( q + 22q^{3} - 25q^{5} + 218q^{7} + 241q^{9} - 480q^{11} - 622q^{13} - 550q^{15} + 186q^{17} - 1204q^{19} + 4796q^{21} - 3186q^{23} + 625q^{25} - 44q^{27} + 5526q^{29} + 9356q^{31} - 10560q^{33} - 5450q^{35} + 5618q^{37} - 13684q^{39} - 14394q^{41} - 370q^{43} - 6025q^{45} + 16146q^{47} + 30717q^{49} + 4092q^{51} - 4374q^{53} + 12000q^{55} - 26488q^{57} - 11748q^{59} + 13202q^{61} + 52538q^{63} + 15550q^{65} - 11542q^{67} - 70092q^{69} - 29532q^{71} + 33698q^{73} + 13750q^{75} - 104640q^{77} + 31208q^{79} - 59531q^{81} - 38466q^{83} - 4650q^{85} + 121572q^{87} + 119514q^{89} - 135596q^{91} + 205832q^{93} + 30100q^{95} + 94658q^{97} - 115680q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(20))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
20.6.a.a \(1\) \(3.208\) \(\Q\) None \(0\) \(22\) \(-25\) \(218\) \(-\) \(+\) \(q+22q^{3}-5^{2}q^{5}+218q^{7}+241q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(20)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 22 T + 243 T^{2} \)
$5$ \( 1 + 25 T \)
$7$ \( 1 - 218 T + 16807 T^{2} \)
$11$ \( 1 + 480 T + 161051 T^{2} \)
$13$ \( 1 + 622 T + 371293 T^{2} \)
$17$ \( 1 - 186 T + 1419857 T^{2} \)
$19$ \( 1 + 1204 T + 2476099 T^{2} \)
$23$ \( 1 + 3186 T + 6436343 T^{2} \)
$29$ \( 1 - 5526 T + 20511149 T^{2} \)
$31$ \( 1 - 9356 T + 28629151 T^{2} \)
$37$ \( 1 - 5618 T + 69343957 T^{2} \)
$41$ \( 1 + 14394 T + 115856201 T^{2} \)
$43$ \( 1 + 370 T + 147008443 T^{2} \)
$47$ \( 1 - 16146 T + 229345007 T^{2} \)
$53$ \( 1 + 4374 T + 418195493 T^{2} \)
$59$ \( 1 + 11748 T + 714924299 T^{2} \)
$61$ \( 1 - 13202 T + 844596301 T^{2} \)
$67$ \( 1 + 11542 T + 1350125107 T^{2} \)
$71$ \( 1 + 29532 T + 1804229351 T^{2} \)
$73$ \( 1 - 33698 T + 2073071593 T^{2} \)
$79$ \( 1 - 31208 T + 3077056399 T^{2} \)
$83$ \( 1 + 38466 T + 3939040643 T^{2} \)
$89$ \( 1 - 119514 T + 5584059449 T^{2} \)
$97$ \( 1 - 94658 T + 8587340257 T^{2} \)
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