Properties

Label 1824.2.a.j
Level $1824$
Weight $2$
Character orbit 1824.a
Self dual yes
Analytic conductor $14.565$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1824.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.5647133287\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + q^{3} + q^{9} + O(q^{10}) \) \( q + q^{3} + q^{9} - 2q^{17} + q^{19} + 6q^{23} - 5q^{25} + q^{27} + 10q^{29} + 10q^{31} + 8q^{37} + 6q^{41} - 4q^{43} - 6q^{47} - 7q^{49} - 2q^{51} - 6q^{53} + q^{57} + 12q^{59} - 10q^{61} + 8q^{67} + 6q^{69} + 8q^{71} - 2q^{73} - 5q^{75} + 6q^{79} + q^{81} + 12q^{83} + 10q^{87} - 6q^{89} + 10q^{93} - 2q^{97} + O(q^{100}) \)

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 1.00000 0 0 0 0 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(19\) \(-1\)

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 1824.2.a.j yes 1
3.b odd 2 1 5472.2.a.k 1
4.b odd 2 1 1824.2.a.d 1
8.b even 2 1 3648.2.a.k 1
8.d odd 2 1 3648.2.a.ba 1
12.b even 2 1 5472.2.a.j 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1824.2.a.d 1 4.b odd 2 1
1824.2.a.j yes 1 1.a even 1 1 trivial
3648.2.a.k 1 8.b even 2 1
3648.2.a.ba 1 8.d odd 2 1
5472.2.a.j 1 12.b even 2 1
5472.2.a.k 1 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1824))\):

\( T_{5} \)
\( T_{7} \)
\( T_{11} \)
\( T_{23} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -1 + T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( T \)
$13$ \( T \)
$17$ \( 2 + T \)
$19$ \( -1 + T \)
$23$ \( -6 + T \)
$29$ \( -10 + T \)
$31$ \( -10 + T \)
$37$ \( -8 + T \)
$41$ \( -6 + T \)
$43$ \( 4 + T \)
$47$ \( 6 + T \)
$53$ \( 6 + T \)
$59$ \( -12 + T \)
$61$ \( 10 + T \)
$67$ \( -8 + T \)
$71$ \( -8 + T \)
$73$ \( 2 + T \)
$79$ \( -6 + T \)
$83$ \( -12 + T \)
$89$ \( 6 + T \)
$97$ \( 2 + T \)
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