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

Related objects

Downloads

Learn more about

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

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

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 \(S_{6}^{\mathrm{new}}(\Gamma_0(20))\).