Properties

Label 574.2.a.i
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} - 2q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} - 2q^{9} + q^{10} + 2q^{11} - q^{12} + 4q^{13} + q^{14} - q^{15} + q^{16} + 3q^{17} - 2q^{18} + q^{20} - q^{21} + 2q^{22} + 4q^{23} - q^{24} - 4q^{25} + 4q^{26} + 5q^{27} + q^{28} - 5q^{29} - q^{30} + 7q^{31} + q^{32} - 2q^{33} + 3q^{34} + q^{35} - 2q^{36} - 2q^{37} - 4q^{39} + q^{40} + q^{41} - q^{42} - q^{43} + 2q^{44} - 2q^{45} + 4q^{46} - 2q^{47} - q^{48} + q^{49} - 4q^{50} - 3q^{51} + 4q^{52} - q^{53} + 5q^{54} + 2q^{55} + q^{56} - 5q^{58} + 10q^{59} - q^{60} - 13q^{61} + 7q^{62} - 2q^{63} + q^{64} + 4q^{65} - 2q^{66} - 2q^{67} + 3q^{68} - 4q^{69} + q^{70} - 3q^{71} - 2q^{72} + 4q^{73} - 2q^{74} + 4q^{75} + 2q^{77} - 4q^{78} - 15q^{79} + q^{80} + q^{81} + q^{82} - 6q^{83} - q^{84} + 3q^{85} - q^{86} + 5q^{87} + 2q^{88} - 15q^{89} - 2q^{90} + 4q^{91} + 4q^{92} - 7q^{93} - 2q^{94} - q^{96} - 7q^{97} + q^{98} - 4q^{99} + O(q^{100}) \)

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

\( T_{3} + 1 \)
\( T_{5} - 1 \)
\( T_{11} - 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( 1 + T \)
$5$ \( -1 + T \)
$7$ \( -1 + T \)
$11$ \( -2 + T \)
$13$ \( -4 + T \)
$17$ \( -3 + T \)
$19$ \( T \)
$23$ \( -4 + T \)
$29$ \( 5 + T \)
$31$ \( -7 + T \)
$37$ \( 2 + T \)
$41$ \( -1 + T \)
$43$ \( 1 + T \)
$47$ \( 2 + T \)
$53$ \( 1 + T \)
$59$ \( -10 + T \)
$61$ \( 13 + T \)
$67$ \( 2 + T \)
$71$ \( 3 + T \)
$73$ \( -4 + T \)
$79$ \( 15 + T \)
$83$ \( 6 + T \)
$89$ \( 15 + T \)
$97$ \( 7 + T \)
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