Properties

Label 6034.2.a.f
Level 6034
Weight 2
Character orbit 6034.a
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
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

\(f(q)\) \(=\) \( q + q^{2} + 3q^{3} + q^{4} + 2q^{5} + 3q^{6} - q^{7} + q^{8} + 6q^{9} + O(q^{10}) \) \( q + q^{2} + 3q^{3} + q^{4} + 2q^{5} + 3q^{6} - q^{7} + q^{8} + 6q^{9} + 2q^{10} + 3q^{12} + q^{13} - q^{14} + 6q^{15} + q^{16} - 2q^{17} + 6q^{18} - 7q^{19} + 2q^{20} - 3q^{21} + 6q^{23} + 3q^{24} - q^{25} + q^{26} + 9q^{27} - q^{28} + 5q^{29} + 6q^{30} + 2q^{31} + q^{32} - 2q^{34} - 2q^{35} + 6q^{36} + 8q^{37} - 7q^{38} + 3q^{39} + 2q^{40} - 3q^{42} - 9q^{43} + 12q^{45} + 6q^{46} + 6q^{47} + 3q^{48} + q^{49} - q^{50} - 6q^{51} + q^{52} + 10q^{53} + 9q^{54} - q^{56} - 21q^{57} + 5q^{58} + 4q^{59} + 6q^{60} + 8q^{61} + 2q^{62} - 6q^{63} + q^{64} + 2q^{65} + q^{67} - 2q^{68} + 18q^{69} - 2q^{70} - 15q^{71} + 6q^{72} + 9q^{73} + 8q^{74} - 3q^{75} - 7q^{76} + 3q^{78} + q^{79} + 2q^{80} + 9q^{81} + 8q^{83} - 3q^{84} - 4q^{85} - 9q^{86} + 15q^{87} - 10q^{89} + 12q^{90} - q^{91} + 6q^{92} + 6q^{93} + 6q^{94} - 14q^{95} + 3q^{96} + 16q^{97} + q^{98} + O(q^{100}) \)

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 3.00000 1.00000 2.00000 3.00000 −1.00000 1.00000 6.00000 2.00000
\(n\): 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
\(2\) \(-1\)
\(7\) \(1\)
\(431\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\):

\( T_{3} - 3 \)
\( T_{5} - 2 \)
\( T_{11} \)