Properties

Label 20.4.a.a
Level 20
Weight 4
Character orbit 20.a
Self dual Yes
Analytic conductor 1.180
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 20.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.18003820011\)
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

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

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 4.00000 0 5.00000 0 −16.0000 0 −11.0000 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(20))\).