Properties

Label 418.2.a.b
Level $418$
Weight $2$
Character orbit 418.a
Self dual yes
Analytic conductor $3.338$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.33774680449\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + 2 q^{5} + 2 q^{7} + q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{4} + 2 q^{5} + 2 q^{7} + q^{8} - 3 q^{9} + 2 q^{10} + q^{11} - 2 q^{13} + 2 q^{14} + q^{16} + 6 q^{17} - 3 q^{18} + q^{19} + 2 q^{20} + q^{22} - 8 q^{23} - q^{25} - 2 q^{26} + 2 q^{28} - 6 q^{29} + 6 q^{31} + q^{32} + 6 q^{34} + 4 q^{35} - 3 q^{36} + 8 q^{37} + q^{38} + 2 q^{40} + 6 q^{41} - 8 q^{43} + q^{44} - 6 q^{45} - 8 q^{46} - 8 q^{47} - 3 q^{49} - q^{50} - 2 q^{52} + 12 q^{53} + 2 q^{55} + 2 q^{56} - 6 q^{58} - 8 q^{61} + 6 q^{62} - 6 q^{63} + q^{64} - 4 q^{65} - 8 q^{67} + 6 q^{68} + 4 q^{70} - 6 q^{71} - 3 q^{72} - 14 q^{73} + 8 q^{74} + q^{76} + 2 q^{77} - 12 q^{79} + 2 q^{80} + 9 q^{81} + 6 q^{82} - 12 q^{83} + 12 q^{85} - 8 q^{86} + q^{88} + 2 q^{89} - 6 q^{90} - 4 q^{91} - 8 q^{92} - 8 q^{94} + 2 q^{95} - 2 q^{97} - 3 q^{98} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 2.00000 0 2.00000 1.00000 −3.00000 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(11\) \(-1\)
\(19\) \(-1\)

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 418.2.a.b 1
3.b odd 2 1 3762.2.a.c 1
4.b odd 2 1 3344.2.a.g 1
11.b odd 2 1 4598.2.a.f 1
19.b odd 2 1 7942.2.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
418.2.a.b 1 1.a even 1 1 trivial
3344.2.a.g 1 4.b odd 2 1
3762.2.a.c 1 3.b odd 2 1
4598.2.a.f 1 11.b odd 2 1
7942.2.a.g 1 19.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(418))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 1 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 2 \) Copy content Toggle raw display
$7$ \( T - 2 \) Copy content Toggle raw display
$11$ \( T - 1 \) Copy content Toggle raw display
$13$ \( T + 2 \) Copy content Toggle raw display
$17$ \( T - 6 \) Copy content Toggle raw display
$19$ \( T - 1 \) Copy content Toggle raw display
$23$ \( T + 8 \) Copy content Toggle raw display
$29$ \( T + 6 \) Copy content Toggle raw display
$31$ \( T - 6 \) Copy content Toggle raw display
$37$ \( T - 8 \) Copy content Toggle raw display
$41$ \( T - 6 \) Copy content Toggle raw display
$43$ \( T + 8 \) Copy content Toggle raw display
$47$ \( T + 8 \) Copy content Toggle raw display
$53$ \( T - 12 \) Copy content Toggle raw display
$59$ \( T \) Copy content Toggle raw display
$61$ \( T + 8 \) Copy content Toggle raw display
$67$ \( T + 8 \) Copy content Toggle raw display
$71$ \( T + 6 \) Copy content Toggle raw display
$73$ \( T + 14 \) Copy content Toggle raw display
$79$ \( T + 12 \) Copy content Toggle raw display
$83$ \( T + 12 \) Copy content Toggle raw display
$89$ \( T - 2 \) Copy content Toggle raw display
$97$ \( T + 2 \) Copy content Toggle raw display
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