Properties

Label 574.2.a.h
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: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

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

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(574))\):

\( T_{3} + 1 \)
\( T_{5} + 1 \)
\( T_{11} + 6 \)