Properties

Label 20.10.a.a
Level 20
Weight 10
Character orbit 20.a
Self dual Yes
Analytic conductor 10.301
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 20.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(10.3007167233\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 48q^{3} \) \(\mathstrut +\mathstrut 625q^{5} \) \(\mathstrut -\mathstrut 532q^{7} \) \(\mathstrut -\mathstrut 17379q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 48q^{3} \) \(\mathstrut +\mathstrut 625q^{5} \) \(\mathstrut -\mathstrut 532q^{7} \) \(\mathstrut -\mathstrut 17379q^{9} \) \(\mathstrut -\mathstrut 33180q^{11} \) \(\mathstrut -\mathstrut 99682q^{13} \) \(\mathstrut -\mathstrut 30000q^{15} \) \(\mathstrut -\mathstrut 443454q^{17} \) \(\mathstrut -\mathstrut 357244q^{19} \) \(\mathstrut +\mathstrut 25536q^{21} \) \(\mathstrut -\mathstrut 142956q^{23} \) \(\mathstrut +\mathstrut 390625q^{25} \) \(\mathstrut +\mathstrut 1778976q^{27} \) \(\mathstrut +\mathstrut 1527966q^{29} \) \(\mathstrut +\mathstrut 7323416q^{31} \) \(\mathstrut +\mathstrut 1592640q^{33} \) \(\mathstrut -\mathstrut 332500q^{35} \) \(\mathstrut -\mathstrut 2666842q^{37} \) \(\mathstrut +\mathstrut 4784736q^{39} \) \(\mathstrut -\mathstrut 7939014q^{41} \) \(\mathstrut -\mathstrut 21174520q^{43} \) \(\mathstrut -\mathstrut 10861875q^{45} \) \(\mathstrut +\mathstrut 16059636q^{47} \) \(\mathstrut -\mathstrut 40070583q^{49} \) \(\mathstrut +\mathstrut 21285792q^{51} \) \(\mathstrut -\mathstrut 87822234q^{53} \) \(\mathstrut -\mathstrut 20737500q^{55} \) \(\mathstrut +\mathstrut 17147712q^{57} \) \(\mathstrut +\mathstrut 120625212q^{59} \) \(\mathstrut +\mathstrut 93576542q^{61} \) \(\mathstrut +\mathstrut 9245628q^{63} \) \(\mathstrut -\mathstrut 62301250q^{65} \) \(\mathstrut +\mathstrut 193621688q^{67} \) \(\mathstrut +\mathstrut 6861888q^{69} \) \(\mathstrut +\mathstrut 417763488q^{71} \) \(\mathstrut -\mathstrut 450372742q^{73} \) \(\mathstrut -\mathstrut 18750000q^{75} \) \(\mathstrut +\mathstrut 17651760q^{77} \) \(\mathstrut -\mathstrut 91425472q^{79} \) \(\mathstrut +\mathstrut 256680009q^{81} \) \(\mathstrut -\mathstrut 652637376q^{83} \) \(\mathstrut -\mathstrut 277158750q^{85} \) \(\mathstrut -\mathstrut 73342368q^{87} \) \(\mathstrut -\mathstrut 170059206q^{89} \) \(\mathstrut +\mathstrut 53030824q^{91} \) \(\mathstrut -\mathstrut 351523968q^{93} \) \(\mathstrut -\mathstrut 223277500q^{95} \) \(\mathstrut -\mathstrut 10947022q^{97} \) \(\mathstrut +\mathstrut 576635220q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −48.0000 0 625.000 0 −532.000 0 −17379.0 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 \(T_{3} \) \(\mathstrut +\mathstrut 48 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(20))\).