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

Related objects

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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: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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 −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.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 20.10.a.a 1
3.b odd 2 1 180.10.a.b 1
4.b odd 2 1 80.10.a.c 1
5.b even 2 1 100.10.a.b 1
5.c odd 4 2 100.10.c.b 2
8.b even 2 1 320.10.a.g 1
8.d odd 2 1 320.10.a.d 1
20.d odd 2 1 400.10.a.e 1
20.e even 4 2 400.10.c.h 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
20.10.a.a 1 1.a even 1 1 trivial
80.10.a.c 1 4.b odd 2 1
100.10.a.b 1 5.b even 2 1
100.10.c.b 2 5.c odd 4 2
180.10.a.b 1 3.b odd 2 1
320.10.a.d 1 8.d odd 2 1
320.10.a.g 1 8.b even 2 1
400.10.a.e 1 20.d odd 2 1
400.10.c.h 2 20.e even 4 2

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 48 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(20))\).