Properties

Label 1334.2.a.a
Level $1334$
Weight $2$
Character orbit 1334.a
Self dual yes
Analytic conductor $10.652$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.6520436296\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + 4q^{7} - q^{8} - 3q^{9} + O(q^{10}) \) \( q - q^{2} + q^{4} + 4q^{7} - q^{8} - 3q^{9} + 2q^{11} + 6q^{13} - 4q^{14} + q^{16} + 2q^{17} + 3q^{18} - 2q^{19} - 2q^{22} + q^{23} - 5q^{25} - 6q^{26} + 4q^{28} - q^{29} - q^{32} - 2q^{34} - 3q^{36} + 4q^{37} + 2q^{38} - 2q^{41} + 10q^{43} + 2q^{44} - q^{46} + 8q^{47} + 9q^{49} + 5q^{50} + 6q^{52} - 8q^{53} - 4q^{56} + q^{58} - 4q^{59} - 8q^{61} - 12q^{63} + q^{64} + 2q^{67} + 2q^{68} - 8q^{71} + 3q^{72} + 6q^{73} - 4q^{74} - 2q^{76} + 8q^{77} + 8q^{79} + 9q^{81} + 2q^{82} - 6q^{83} - 10q^{86} - 2q^{88} + 6q^{89} + 24q^{91} + q^{92} - 8q^{94} + 18q^{97} - 9q^{98} - 6q^{99} + O(q^{100}) \)

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
−1.00000 0 1.00000 0 0 4.00000 −1.00000 −3.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(23\) \(-1\)
\(29\) \(1\)

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 1334.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1334.2.a.a 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1334))\):

\( T_{3} \)
\( T_{5} \)

Hecke characteristic polynomials

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