Properties

Label 14.2.a.a
Level 14
Weight 2
Character orbit 14.a
Self dual Yes
Analytic conductor 0.112
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 14.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.11179056283\)
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

\(f(q)\) \(=\) \( q - q^{2} - 2q^{3} + q^{4} + 2q^{6} + q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - 2q^{3} + q^{4} + 2q^{6} + q^{7} - q^{8} + q^{9} - 2q^{12} - 4q^{13} - q^{14} + q^{16} + 6q^{17} - q^{18} + 2q^{19} - 2q^{21} + 2q^{24} - 5q^{25} + 4q^{26} + 4q^{27} + q^{28} - 6q^{29} - 4q^{31} - q^{32} - 6q^{34} + q^{36} + 2q^{37} - 2q^{38} + 8q^{39} + 6q^{41} + 2q^{42} + 8q^{43} - 12q^{47} - 2q^{48} + q^{49} + 5q^{50} - 12q^{51} - 4q^{52} + 6q^{53} - 4q^{54} - q^{56} - 4q^{57} + 6q^{58} - 6q^{59} + 8q^{61} + 4q^{62} + q^{63} + q^{64} - 4q^{67} + 6q^{68} - q^{72} + 2q^{73} - 2q^{74} + 10q^{75} + 2q^{76} - 8q^{78} + 8q^{79} - 11q^{81} - 6q^{82} - 6q^{83} - 2q^{84} - 8q^{86} + 12q^{87} - 6q^{89} - 4q^{91} + 8q^{93} + 12q^{94} + 2q^{96} - 10q^{97} - q^{98} + O(q^{100}) \)

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 −2.00000 1.00000 0 2.00000 1.00000 −1.00000 1.00000 0
\(n\): 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
\(2\) \(1\)
\(7\) \(-1\)

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\).