Properties

Label 6008.2.a.b
Level 6008
Weight 2
Character orbit 6008.a
Self dual Yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 0 −3.30487 0 0.148423 0 −4.48376 0 7.92214 0
1.2 0 −3.25541 0 3.98380 0 −3.42108 0 7.59768 0
1.3 0 −3.25538 0 −1.89943 0 −1.94419 0 7.59748 0
1.4 0 −3.18197 0 −2.41204 0 2.14400 0 7.12495 0
1.5 0 −2.99842 0 0.770002 0 1.05287 0 5.99050 0
1.6 0 −2.98092 0 3.05916 0 0.297244 0 5.88586 0
1.7 0 −2.46379 0 1.54615 0 −4.51355 0 3.07028 0
1.8 0 −2.32283 0 3.89591 0 0.0996640 0 2.39554 0
1.9 0 −2.25093 0 3.53241 0 1.19008 0 2.06668 0
1.10 0 −2.12121 0 −1.44700 0 4.49803 0 1.49952 0
1.11 0 −2.09991 0 −2.89043 0 −1.97185 0 1.40961 0
1.12 0 −2.01203 0 −4.06513 0 −4.33062 0 1.04828 0
1.13 0 −2.00709 0 0.0492234 0 3.84191 0 1.02840 0
1.14 0 −1.75295 0 1.89627 0 −3.72975 0 0.0728254 0
1.15 0 −1.61777 0 −2.18000 0 −2.82839 0 −0.382806 0
1.16 0 −1.52846 0 0.276340 0 2.37933 0 −0.663805 0
1.17 0 −1.09930 0 −2.74603 0 2.16897 0 −1.79154 0
1.18 0 −1.03287 0 −2.90339 0 −0.294834 0 −1.93318 0
1.19 0 −0.962699 0 2.73078 0 −4.42659 0 −2.07321 0
1.20 0 −0.753945 0 −1.16579 0 1.19034 0 −2.43157 0
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.44
Significant digits:
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Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(751\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{44} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6008))\).