Properties

Label 20.6.a.a
Level 20
Weight 6
Character orbit 20.a
Self dual Yes
Analytic conductor 3.208
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 20.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(3.20767639626\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 22.0000 0 −25.0000 0 218.000 0 241.000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)

Hecke kernels

There are no other newforms in \(S_{6}^{\mathrm{new}}(\Gamma_0(20))\).