Properties

Label 1449.2.a.a
Level $1449$
Weight $2$
Character orbit 1449.a
Self dual yes
Analytic conductor $11.570$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1449.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5703232529\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 483)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2 q^{2} + 2 q^{4} - 4 q^{5} - q^{7} + O(q^{10}) \) \( q - 2 q^{2} + 2 q^{4} - 4 q^{5} - q^{7} + 8 q^{10} + 5 q^{11} - 2 q^{13} + 2 q^{14} - 4 q^{16} - 5 q^{19} - 8 q^{20} - 10 q^{22} + q^{23} + 11 q^{25} + 4 q^{26} - 2 q^{28} + 2 q^{29} + 6 q^{31} + 8 q^{32} + 4 q^{35} + 6 q^{37} + 10 q^{38} - 5 q^{41} + 8 q^{43} + 10 q^{44} - 2 q^{46} + 9 q^{47} + q^{49} - 22 q^{50} - 4 q^{52} - 9 q^{53} - 20 q^{55} - 4 q^{58} - 9 q^{59} - 5 q^{61} - 12 q^{62} - 8 q^{64} + 8 q^{65} + 4 q^{67} - 8 q^{70} - 12 q^{71} - 12 q^{74} - 10 q^{76} - 5 q^{77} - 10 q^{79} + 16 q^{80} + 10 q^{82} + 18 q^{83} - 16 q^{86} - 10 q^{89} + 2 q^{91} + 2 q^{92} - 18 q^{94} + 20 q^{95} - 18 q^{97} - 2 q^{98} + O(q^{100}) \)

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 2.00000 −4.00000 0 −1.00000 0 0 8.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 1449.2.a.a 1
3.b odd 2 1 483.2.a.b 1
12.b even 2 1 7728.2.a.l 1
21.c even 2 1 3381.2.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.a.b 1 3.b odd 2 1
1449.2.a.a 1 1.a even 1 1 trivial
3381.2.a.l 1 21.c even 2 1
7728.2.a.l 1 12.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1449))\):

\( T_{2} + 2 \)
\( T_{5} + 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 2 + T \)
$3$ \( T \)
$5$ \( 4 + T \)
$7$ \( 1 + T \)
$11$ \( -5 + T \)
$13$ \( 2 + T \)
$17$ \( T \)
$19$ \( 5 + T \)
$23$ \( -1 + T \)
$29$ \( -2 + T \)
$31$ \( -6 + T \)
$37$ \( -6 + T \)
$41$ \( 5 + T \)
$43$ \( -8 + T \)
$47$ \( -9 + T \)
$53$ \( 9 + T \)
$59$ \( 9 + T \)
$61$ \( 5 + T \)
$67$ \( -4 + T \)
$71$ \( 12 + T \)
$73$ \( T \)
$79$ \( 10 + T \)
$83$ \( -18 + T \)
$89$ \( 10 + T \)
$97$ \( 18 + T \)
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