Properties

Label 2070.4.a.e
Level $2070$
Weight $4$
Character orbit 2070.a
Self dual yes
Analytic conductor $122.134$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2070.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(122.133953712\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2 q^{2} + 4 q^{4} + 5 q^{5} - 18 q^{7} - 8 q^{8} + O(q^{10}) \) \( q - 2 q^{2} + 4 q^{4} + 5 q^{5} - 18 q^{7} - 8 q^{8} - 10 q^{10} + 32 q^{11} - 47 q^{13} + 36 q^{14} + 16 q^{16} - 20 q^{17} + 36 q^{19} + 20 q^{20} - 64 q^{22} + 23 q^{23} + 25 q^{25} + 94 q^{26} - 72 q^{28} + 27 q^{29} - 33 q^{31} - 32 q^{32} + 40 q^{34} - 90 q^{35} + 56 q^{37} - 72 q^{38} - 40 q^{40} + 157 q^{41} + 18 q^{43} + 128 q^{44} - 46 q^{46} - 65 q^{47} - 19 q^{49} - 50 q^{50} - 188 q^{52} + 14 q^{53} + 160 q^{55} + 144 q^{56} - 54 q^{58} + 744 q^{59} + 552 q^{61} + 66 q^{62} + 64 q^{64} - 235 q^{65} - 156 q^{67} - 80 q^{68} + 180 q^{70} - 699 q^{71} - 609 q^{73} - 112 q^{74} + 144 q^{76} - 576 q^{77} - 644 q^{79} + 80 q^{80} - 314 q^{82} - 512 q^{83} - 100 q^{85} - 36 q^{86} - 256 q^{88} + 102 q^{89} + 846 q^{91} + 92 q^{92} + 130 q^{94} + 180 q^{95} + 578 q^{97} + 38 q^{98} + O(q^{100}) \)

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
−2.00000 0 4.00000 5.00000 0 −18.0000 −8.00000 0 −10.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(5\) \(-1\)
\(23\) \(-1\)

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 2070.4.a.e 1
3.b odd 2 1 230.4.a.e 1
12.b even 2 1 1840.4.a.d 1
15.d odd 2 1 1150.4.a.b 1
15.e even 4 2 1150.4.b.f 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.4.a.e 1 3.b odd 2 1
1150.4.a.b 1 15.d odd 2 1
1150.4.b.f 2 15.e even 4 2
1840.4.a.d 1 12.b even 2 1
2070.4.a.e 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2070))\):

\( T_{7} + 18 \)
\( T_{11} - 32 \)
\( T_{17} + 20 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 2 + T \)
$3$ \( T \)
$5$ \( -5 + T \)
$7$ \( 18 + T \)
$11$ \( -32 + T \)
$13$ \( 47 + T \)
$17$ \( 20 + T \)
$19$ \( -36 + T \)
$23$ \( -23 + T \)
$29$ \( -27 + T \)
$31$ \( 33 + T \)
$37$ \( -56 + T \)
$41$ \( -157 + T \)
$43$ \( -18 + T \)
$47$ \( 65 + T \)
$53$ \( -14 + T \)
$59$ \( -744 + T \)
$61$ \( -552 + T \)
$67$ \( 156 + T \)
$71$ \( 699 + T \)
$73$ \( 609 + T \)
$79$ \( 644 + T \)
$83$ \( 512 + T \)
$89$ \( -102 + T \)
$97$ \( -578 + T \)
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