Properties

Label 2898.2.a.e
Level $2898$
Weight $2$
Character orbit 2898.a
Self dual yes
Analytic conductor $23.141$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2898.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(23.1406465058\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} + 2q^{11} - 5q^{13} - q^{14} + q^{16} - 2q^{17} - 2q^{19} + q^{20} - 2q^{22} + q^{23} - 4q^{25} + 5q^{26} + q^{28} + 5q^{29} - q^{32} + 2q^{34} + q^{35} - 7q^{37} + 2q^{38} - q^{40} - 3q^{41} - 11q^{43} + 2q^{44} - q^{46} - 9q^{47} + q^{49} + 4q^{50} - 5q^{52} - 10q^{53} + 2q^{55} - q^{56} - 5q^{58} + 12q^{59} - 2q^{61} + q^{64} - 5q^{65} - 4q^{67} - 2q^{68} - q^{70} + 6q^{71} + 6q^{73} + 7q^{74} - 2q^{76} + 2q^{77} - 12q^{79} + q^{80} + 3q^{82} - 4q^{83} - 2q^{85} + 11q^{86} - 2q^{88} - 5q^{91} + q^{92} + 9q^{94} - 2q^{95} - 3q^{97} - q^{98} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(1\)
\(7\) \(-1\)
\(23\) \(-1\)

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 2898.2.a.e 1
3.b odd 2 1 2898.2.a.m yes 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2898.2.a.e 1 1.a even 1 1 trivial
2898.2.a.m yes 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2898))\):

\( T_{5} - 1 \)
\( T_{11} - 2 \)
\( T_{13} + 5 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( -1 + T \)
$7$ \( -1 + T \)
$11$ \( -2 + T \)
$13$ \( 5 + T \)
$17$ \( 2 + T \)
$19$ \( 2 + T \)
$23$ \( -1 + T \)
$29$ \( -5 + T \)
$31$ \( T \)
$37$ \( 7 + T \)
$41$ \( 3 + T \)
$43$ \( 11 + T \)
$47$ \( 9 + T \)
$53$ \( 10 + T \)
$59$ \( -12 + T \)
$61$ \( 2 + T \)
$67$ \( 4 + T \)
$71$ \( -6 + T \)
$73$ \( -6 + T \)
$79$ \( 12 + T \)
$83$ \( 4 + T \)
$89$ \( T \)
$97$ \( 3 + T \)
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