Properties

Label 456.2.a.b
Level $456$
Weight $2$
Character orbit 456.a
Self dual yes
Analytic conductor $3.641$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.64117833217\)
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

\(f(q)\) \(=\) \( q - q^{3} + 4q^{5} + 4q^{7} + q^{9} + O(q^{10}) \) \( q - q^{3} + 4q^{5} + 4q^{7} + q^{9} - 4q^{11} - 4q^{13} - 4q^{15} + 6q^{17} + q^{19} - 4q^{21} - 6q^{23} + 11q^{25} - q^{27} + 2q^{29} + 2q^{31} + 4q^{33} + 16q^{35} + 4q^{37} + 4q^{39} - 6q^{41} + 4q^{43} + 4q^{45} - 2q^{47} + 9q^{49} - 6q^{51} - 6q^{53} - 16q^{55} - q^{57} - 4q^{59} - 10q^{61} + 4q^{63} - 16q^{65} + 8q^{67} + 6q^{69} - 2q^{73} - 11q^{75} - 16q^{77} + 14q^{79} + q^{81} - 16q^{83} + 24q^{85} - 2q^{87} - 18q^{89} - 16q^{91} - 2q^{93} + 4q^{95} + 14q^{97} - 4q^{99} + O(q^{100}) \)

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
0 −1.00000 0 4.00000 0 4.00000 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 456.2.a.b 1
3.b odd 2 1 1368.2.a.b 1
4.b odd 2 1 912.2.a.l 1
8.b even 2 1 3648.2.a.s 1
8.d odd 2 1 3648.2.a.a 1
12.b even 2 1 2736.2.a.a 1
19.b odd 2 1 8664.2.a.o 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
456.2.a.b 1 1.a even 1 1 trivial
912.2.a.l 1 4.b odd 2 1
1368.2.a.b 1 3.b odd 2 1
2736.2.a.a 1 12.b even 2 1
3648.2.a.a 1 8.d odd 2 1
3648.2.a.s 1 8.b even 2 1
8664.2.a.o 1 19.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 4 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(456))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 1 + T \)
$5$ \( -4 + T \)
$7$ \( -4 + T \)
$11$ \( 4 + T \)
$13$ \( 4 + T \)
$17$ \( -6 + T \)
$19$ \( -1 + T \)
$23$ \( 6 + T \)
$29$ \( -2 + T \)
$31$ \( -2 + T \)
$37$ \( -4 + T \)
$41$ \( 6 + T \)
$43$ \( -4 + T \)
$47$ \( 2 + T \)
$53$ \( 6 + T \)
$59$ \( 4 + T \)
$61$ \( 10 + T \)
$67$ \( -8 + T \)
$71$ \( T \)
$73$ \( 2 + T \)
$79$ \( -14 + T \)
$83$ \( 16 + T \)
$89$ \( 18 + T \)
$97$ \( -14 + T \)
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