Properties

Label 490.2.a.e
Level 490
Weight 2
Character orbit 490.a
Self dual Yes
Analytic conductor 3.913
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 490.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(3.91266969904\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + q^{2} - 3q^{3} + q^{4} + q^{5} - 3q^{6} + q^{8} + 6q^{9} + O(q^{10}) \) \( q + q^{2} - 3q^{3} + q^{4} + q^{5} - 3q^{6} + q^{8} + 6q^{9} + q^{10} - 2q^{11} - 3q^{12} - 3q^{15} + q^{16} + 4q^{17} + 6q^{18} + 6q^{19} + q^{20} - 2q^{22} + 3q^{23} - 3q^{24} + q^{25} - 9q^{27} + 9q^{29} - 3q^{30} + 4q^{31} + q^{32} + 6q^{33} + 4q^{34} + 6q^{36} - 4q^{37} + 6q^{38} + q^{40} + 7q^{41} - 5q^{43} - 2q^{44} + 6q^{45} + 3q^{46} - 8q^{47} - 3q^{48} + q^{50} - 12q^{51} - 2q^{53} - 9q^{54} - 2q^{55} - 18q^{57} + 9q^{58} - 10q^{59} - 3q^{60} - q^{61} + 4q^{62} + q^{64} + 6q^{66} - 9q^{67} + 4q^{68} - 9q^{69} + 2q^{71} + 6q^{72} + 4q^{73} - 4q^{74} - 3q^{75} + 6q^{76} + 10q^{79} + q^{80} + 9q^{81} + 7q^{82} + 7q^{83} + 4q^{85} - 5q^{86} - 27q^{87} - 2q^{88} - q^{89} + 6q^{90} + 3q^{92} - 12q^{93} - 8q^{94} + 6q^{95} - 3q^{96} - 14q^{97} - 12q^{99} + O(q^{100}) \)

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 −3.00000 1.00000 1.00000 −3.00000 0 1.00000 6.00000 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
\(2\) \(-1\)
\(5\) \(-1\)
\(7\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(490))\):

\( T_{3} + 3 \)
\( T_{11} + 2 \)
\( T_{13} \)