Properties

Label 574.2.a.j
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

Related objects

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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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} - 4q^{5} + q^{7} + q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} + q^{4} - 4q^{5} + q^{7} + q^{8} - 3q^{9} - 4q^{10} - 2q^{11} - 6q^{13} + q^{14} + q^{16} - 6q^{17} - 3q^{18} + 4q^{19} - 4q^{20} - 2q^{22} + 8q^{23} + 11q^{25} - 6q^{26} + q^{28} - 8q^{29} + q^{32} - 6q^{34} - 4q^{35} - 3q^{36} - 2q^{37} + 4q^{38} - 4q^{40} - q^{41} - 8q^{43} - 2q^{44} + 12q^{45} + 8q^{46} + q^{49} + 11q^{50} - 6q^{52} + 8q^{55} + q^{56} - 8q^{58} + 2q^{59} - 8q^{61} - 3q^{63} + q^{64} + 24q^{65} + 10q^{67} - 6q^{68} - 4q^{70} - 12q^{71} - 3q^{72} + 10q^{73} - 2q^{74} + 4q^{76} - 2q^{77} + 16q^{79} - 4q^{80} + 9q^{81} - q^{82} - 2q^{83} + 24q^{85} - 8q^{86} - 2q^{88} - 10q^{89} + 12q^{90} - 6q^{91} + 8q^{92} - 16q^{95} - 2q^{97} + q^{98} + 6q^{99} + O(q^{100}) \)

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 0 1.00000 −4.00000 0 1.00000 1.00000 −3.00000 −4.00000
\(n\): 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(574))\):

\( T_{3} \)
\( T_{5} + 4 \)
\( T_{11} + 2 \)