Properties

Label 20.8.a.a
Level 20
Weight 8
Character orbit 20.a
Self dual Yes
Analytic conductor 6.248
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 20.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(6.24770050968\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q - 6q^{3} - 125q^{5} - 706q^{7} - 2151q^{9} + O(q^{10}) \) \( q - 6q^{3} - 125q^{5} - 706q^{7} - 2151q^{9} - 3840q^{11} - 4054q^{13} + 750q^{15} + 858q^{17} + 21044q^{19} + 4236q^{21} + 85338q^{23} + 15625q^{25} + 26028q^{27} - 83106q^{29} - 145564q^{31} + 23040q^{33} + 88250q^{35} - 498886q^{37} + 24324q^{39} - 689514q^{41} + 867890q^{43} + 268875q^{45} + 235638q^{47} - 325107q^{49} - 5148q^{51} + 1835442q^{53} + 480000q^{55} - 126264q^{57} + 629508q^{59} - 2667958q^{61} + 1518606q^{63} + 506750q^{65} - 3373306q^{67} - 512028q^{69} - 2600052q^{71} - 1628494q^{73} - 93750q^{75} + 2711040q^{77} - 4243528q^{79} + 4548069q^{81} + 1251378q^{83} - 107250q^{85} + 498636q^{87} + 6299466q^{89} + 2862124q^{91} + 873384q^{93} - 2630500q^{95} + 3976514q^{97} + 8259840q^{99} + O(q^{100}) \)

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 −6.00000 0 −125.000 0 −706.000 0 −2151.00 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

This newform can be constructed as the kernel of the linear operator \( T_{3} + 6 \) acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(20))\).