Properties

Label 6930.2.a.a
Level 6930
Weight 2
Character orbit 6930.a
Self dual Yes
Analytic conductor 55.336
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6930.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(55.3363286007\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + q^{11} - 2q^{13} + q^{14} + q^{16} + 6q^{17} - 4q^{19} - q^{20} - q^{22} + q^{25} + 2q^{26} - q^{28} + 2q^{29} - 8q^{31} - q^{32} - 6q^{34} + q^{35} + 6q^{37} + 4q^{38} + q^{40} + 6q^{41} - 4q^{43} + q^{44} - 8q^{47} + q^{49} - q^{50} - 2q^{52} + 2q^{53} - q^{55} + q^{56} - 2q^{58} + 4q^{59} - 2q^{61} + 8q^{62} + q^{64} + 2q^{65} - 4q^{67} + 6q^{68} - q^{70} + 10q^{73} - 6q^{74} - 4q^{76} - q^{77} - 16q^{79} - q^{80} - 6q^{82} - 4q^{83} - 6q^{85} + 4q^{86} - q^{88} + 6q^{89} + 2q^{91} + 8q^{94} + 4q^{95} + 10q^{97} - q^{98} + O(q^{100}) \)

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 0 1.00000 −1.00000 0 −1.00000 −1.00000 0 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
\(2\) \(1\)
\(3\) \(-1\)
\(5\) \(1\)
\(7\) \(1\)
\(11\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6930))\):

\( T_{13} + 2 \)
\( T_{17} - 6 \)
\( T_{19} + 4 \)
\( T_{23} \)
\( T_{29} - 2 \)
\( T_{31} + 8 \)