Properties

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

Related objects

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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: \(2\)
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

\(f(q)\) \(=\) \( q - q^{2} - 3q^{3} + q^{4} - q^{5} + 3q^{6} - q^{7} - q^{8} + 6q^{9} + O(q^{10}) \) \( q - q^{2} - 3q^{3} + q^{4} - q^{5} + 3q^{6} - q^{7} - q^{8} + 6q^{9} + q^{10} - 3q^{11} - 3q^{12} - 4q^{13} + q^{14} + 3q^{15} + q^{16} + 2q^{17} - 6q^{18} - 3q^{19} - q^{20} + 3q^{21} + 3q^{22} - 3q^{23} + 3q^{24} - 4q^{25} + 4q^{26} - 9q^{27} - q^{28} - 3q^{29} - 3q^{30} + 6q^{31} - q^{32} + 9q^{33} - 2q^{34} + q^{35} + 6q^{36} - 8q^{37} + 3q^{38} + 12q^{39} + q^{40} - 6q^{41} - 3q^{42} + 2q^{43} - 3q^{44} - 6q^{45} + 3q^{46} - 2q^{47} - 3q^{48} + q^{49} + 4q^{50} - 6q^{51} - 4q^{52} - 9q^{53} + 9q^{54} + 3q^{55} + q^{56} + 9q^{57} + 3q^{58} + 3q^{59} + 3q^{60} - 2q^{61} - 6q^{62} - 6q^{63} + q^{64} + 4q^{65} - 9q^{66} - 2q^{67} + 2q^{68} + 9q^{69} - q^{70} - 6q^{72} - 14q^{73} + 8q^{74} + 12q^{75} - 3q^{76} + 3q^{77} - 12q^{78} - 10q^{79} - q^{80} + 9q^{81} + 6q^{82} + 6q^{83} + 3q^{84} - 2q^{85} - 2q^{86} + 9q^{87} + 3q^{88} + 6q^{89} + 6q^{90} + 4q^{91} - 3q^{92} - 18q^{93} + 2q^{94} + 3q^{95} + 3q^{96} + q^{97} - q^{98} - 18q^{99} + O(q^{100}) \)

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 −1.00000 −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
\(2\) \(1\)
\(7\) \(1\)
\(431\) \(-1\)

Hecke kernels

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

\( T_{3} + 3 \)
\( T_{5} + 1 \)
\( T_{11} + 3 \)