Properties

Label 1840.2.a.e
Level $1840$
Weight $2$
Character orbit 1840.a
Self dual yes
Analytic conductor $14.692$
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: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.6924739719\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 460)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{5} + q^{7} - 3q^{9} + O(q^{10}) \) \( q - q^{5} + q^{7} - 3q^{9} - 6q^{11} + 6q^{13} + 7q^{17} - 2q^{19} + q^{23} + q^{25} - 5q^{29} - q^{31} - q^{35} - 5q^{37} - 7q^{41} - 8q^{43} + 3q^{45} - 8q^{47} - 6q^{49} + 3q^{53} + 6q^{55} - 13q^{59} - 8q^{61} - 3q^{63} - 6q^{65} + 9q^{67} - 7q^{71} - 2q^{73} - 6q^{77} + 12q^{79} + 9q^{81} + 5q^{83} - 7q^{85} - 12q^{89} + 6q^{91} + 2q^{95} + 2q^{97} + 18q^{99} + O(q^{100}) \)

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 0 0 −1.00000 0 1.00000 0 −3.00000 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 1840.2.a.e 1
4.b odd 2 1 460.2.a.b 1
5.b even 2 1 9200.2.a.q 1
8.b even 2 1 7360.2.a.r 1
8.d odd 2 1 7360.2.a.m 1
12.b even 2 1 4140.2.a.h 1
20.d odd 2 1 2300.2.a.e 1
20.e even 4 2 2300.2.c.g 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
460.2.a.b 1 4.b odd 2 1
1840.2.a.e 1 1.a even 1 1 trivial
2300.2.a.e 1 20.d odd 2 1
2300.2.c.g 2 20.e even 4 2
4140.2.a.h 1 12.b even 2 1
7360.2.a.m 1 8.d odd 2 1
7360.2.a.r 1 8.b even 2 1
9200.2.a.q 1 5.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1840))\):

\( T_{3} \)
\( T_{7} - 1 \)
\( T_{11} + 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( 1 + T \)
$7$ \( -1 + T \)
$11$ \( 6 + T \)
$13$ \( -6 + T \)
$17$ \( -7 + T \)
$19$ \( 2 + T \)
$23$ \( -1 + T \)
$29$ \( 5 + T \)
$31$ \( 1 + T \)
$37$ \( 5 + T \)
$41$ \( 7 + T \)
$43$ \( 8 + T \)
$47$ \( 8 + T \)
$53$ \( -3 + T \)
$59$ \( 13 + T \)
$61$ \( 8 + T \)
$67$ \( -9 + T \)
$71$ \( 7 + T \)
$73$ \( 2 + T \)
$79$ \( -12 + T \)
$83$ \( -5 + T \)
$89$ \( 12 + T \)
$97$ \( -2 + T \)
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