Properties

Label 1840.4.a.f
Level $1840$
Weight $4$
Character orbit 1840.a
Self dual yes
Analytic conductor $108.564$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1840.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(108.563514411\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 115)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 3 q^{3} + 5 q^{5} + 2 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 3 q^{3} + 5 q^{5} + 2 q^{7} - 18 q^{9} + 16 q^{11} - 47 q^{13} + 15 q^{15} - 24 q^{17} + 56 q^{19} + 6 q^{21} + 23 q^{23} + 25 q^{25} - 135 q^{27} + 85 q^{29} - 67 q^{31} + 48 q^{33} + 10 q^{35} + 104 q^{37} - 141 q^{39} - 53 q^{41} + 234 q^{43} - 90 q^{45} - 285 q^{47} - 339 q^{49} - 72 q^{51} + 2 q^{53} + 80 q^{55} + 168 q^{57} - 80 q^{59} - 764 q^{61} - 36 q^{63} - 235 q^{65} - 236 q^{67} + 69 q^{69} + 289 q^{71} - 225 q^{73} + 75 q^{75} + 32 q^{77} - 24 q^{79} + 81 q^{81} - 684 q^{83} - 120 q^{85} + 255 q^{87} - 1370 q^{89} - 94 q^{91} - 201 q^{93} + 280 q^{95} - 110 q^{97} - 288 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 3.00000 0 5.00000 0 2.00000 0 −18.0000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 1840.4.a.f 1
4.b odd 2 1 115.4.a.b 1
12.b even 2 1 1035.4.a.a 1
20.d odd 2 1 575.4.a.a 1
20.e even 4 2 575.4.b.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
115.4.a.b 1 4.b odd 2 1
575.4.a.a 1 20.d odd 2 1
575.4.b.a 2 20.e even 4 2
1035.4.a.a 1 12.b even 2 1
1840.4.a.f 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1840))\):

\( T_{3} - 3 \) Copy content Toggle raw display
\( T_{7} - 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 3 \) Copy content Toggle raw display
$5$ \( T - 5 \) Copy content Toggle raw display
$7$ \( T - 2 \) Copy content Toggle raw display
$11$ \( T - 16 \) Copy content Toggle raw display
$13$ \( T + 47 \) Copy content Toggle raw display
$17$ \( T + 24 \) Copy content Toggle raw display
$19$ \( T - 56 \) Copy content Toggle raw display
$23$ \( T - 23 \) Copy content Toggle raw display
$29$ \( T - 85 \) Copy content Toggle raw display
$31$ \( T + 67 \) Copy content Toggle raw display
$37$ \( T - 104 \) Copy content Toggle raw display
$41$ \( T + 53 \) Copy content Toggle raw display
$43$ \( T - 234 \) Copy content Toggle raw display
$47$ \( T + 285 \) Copy content Toggle raw display
$53$ \( T - 2 \) Copy content Toggle raw display
$59$ \( T + 80 \) Copy content Toggle raw display
$61$ \( T + 764 \) Copy content Toggle raw display
$67$ \( T + 236 \) Copy content Toggle raw display
$71$ \( T - 289 \) Copy content Toggle raw display
$73$ \( T + 225 \) Copy content Toggle raw display
$79$ \( T + 24 \) Copy content Toggle raw display
$83$ \( T + 684 \) Copy content Toggle raw display
$89$ \( T + 1370 \) Copy content Toggle raw display
$97$ \( T + 110 \) Copy content Toggle raw display
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