Properties

Label 574.2.a.c
Level $574$
Weight $2$
Character orbit 574.a
Self dual yes
Analytic conductor $4.583$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - 3q^{5} - q^{6} + q^{7} - q^{8} - 2q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} - 3q^{5} - q^{6} + q^{7} - q^{8} - 2q^{9} + 3q^{10} + q^{12} + 2q^{13} - q^{14} - 3q^{15} + q^{16} - 3q^{17} + 2q^{18} - 4q^{19} - 3q^{20} + q^{21} - 6q^{23} - q^{24} + 4q^{25} - 2q^{26} - 5q^{27} + q^{28} - 3q^{29} + 3q^{30} - q^{31} - q^{32} + 3q^{34} - 3q^{35} - 2q^{36} - 4q^{37} + 4q^{38} + 2q^{39} + 3q^{40} + q^{41} - q^{42} - q^{43} + 6q^{45} + 6q^{46} - 6q^{47} + q^{48} + q^{49} - 4q^{50} - 3q^{51} + 2q^{52} + 9q^{53} + 5q^{54} - q^{56} - 4q^{57} + 3q^{58} - 6q^{59} - 3q^{60} - q^{61} + q^{62} - 2q^{63} + q^{64} - 6q^{65} + 8q^{67} - 3q^{68} - 6q^{69} + 3q^{70} + 3q^{71} + 2q^{72} - 10q^{73} + 4q^{74} + 4q^{75} - 4q^{76} - 2q^{78} - q^{79} - 3q^{80} + q^{81} - q^{82} - 12q^{83} + q^{84} + 9q^{85} + q^{86} - 3q^{87} + 3q^{89} - 6q^{90} + 2q^{91} - 6q^{92} - q^{93} + 6q^{94} + 12q^{95} - q^{96} - q^{97} - q^{98} + O(q^{100}) \)

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
−1.00000 1.00000 1.00000 −3.00000 −1.00000 1.00000 −1.00000 −2.00000 3.00000
\(n\): 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.c 1
3.b odd 2 1 5166.2.a.bm 1
4.b odd 2 1 4592.2.a.d 1
7.b odd 2 1 4018.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
574.2.a.c 1 1.a even 1 1 trivial
4018.2.a.f 1 7.b odd 2 1
4592.2.a.d 1 4.b odd 2 1
5166.2.a.bm 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(574))\):

\( T_{3} - 1 \)
\( T_{5} + 3 \)
\( T_{11} \)

Hecke characteristic polynomials

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