Properties

Label 574.2.a.e
Level $574$
Weight $2$
Character orbit 574.a
Self dual yes
Analytic conductor $4.583$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 574 = 2 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 574.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.58341307602\)
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

\(f(q)\) \(=\) \( q - q^{2} + 2q^{3} + q^{4} + 2q^{5} - 2q^{6} + q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + 2q^{3} + q^{4} + 2q^{5} - 2q^{6} + q^{7} - q^{8} + q^{9} - 2q^{10} - 2q^{11} + 2q^{12} + 4q^{13} - q^{14} + 4q^{15} + q^{16} + 6q^{17} - q^{18} - 6q^{19} + 2q^{20} + 2q^{21} + 2q^{22} + 8q^{23} - 2q^{24} - q^{25} - 4q^{26} - 4q^{27} + q^{28} - 4q^{29} - 4q^{30} - 8q^{31} - q^{32} - 4q^{33} - 6q^{34} + 2q^{35} + q^{36} + 10q^{37} + 6q^{38} + 8q^{39} - 2q^{40} - q^{41} - 2q^{42} - 4q^{43} - 2q^{44} + 2q^{45} - 8q^{46} + 8q^{47} + 2q^{48} + q^{49} + q^{50} + 12q^{51} + 4q^{52} - 8q^{53} + 4q^{54} - 4q^{55} - q^{56} - 12q^{57} + 4q^{58} - 4q^{59} + 4q^{60} - 10q^{61} + 8q^{62} + q^{63} + q^{64} + 8q^{65} + 4q^{66} - 2q^{67} + 6q^{68} + 16q^{69} - 2q^{70} + 12q^{71} - q^{72} + 10q^{73} - 10q^{74} - 2q^{75} - 6q^{76} - 2q^{77} - 8q^{78} + 2q^{80} - 11q^{81} + q^{82} + 2q^{84} + 12q^{85} + 4q^{86} - 8q^{87} + 2q^{88} + 18q^{89} - 2q^{90} + 4q^{91} + 8q^{92} - 16q^{93} - 8q^{94} - 12q^{95} - 2q^{96} - 10q^{97} - q^{98} - 2q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(-1\)
\(41\) \(1\)

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 574.2.a.e 1
3.b odd 2 1 5166.2.a.z 1
4.b odd 2 1 4592.2.a.c 1
7.b odd 2 1 4018.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
574.2.a.e 1 1.a even 1 1 trivial
4018.2.a.c 1 7.b odd 2 1
4592.2.a.c 1 4.b odd 2 1
5166.2.a.z 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(574))\):

\( T_{3} - 2 \)
\( T_{5} - 2 \)
\( T_{11} + 2 \)

Hecke characteristic polynomials

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