Properties

Label 354.5.d.a
Level 354
Weight 5
Character orbit 354.d
Analytic conductor 36.593
Analytic rank 0
Dimension 40
CM No

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Newspace parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 354.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(36.5929669317\)
Analytic rank: \(0\)
Dimension: \(40\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40q - 320q^{4} - 80q^{7} + 1080q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 40q - 320q^{4} - 80q^{7} + 1080q^{9} - 144q^{15} + 2560q^{16} + 480q^{17} - 792q^{19} - 1024q^{22} + 3400q^{25} + 768q^{26} + 640q^{28} + 1608q^{29} - 5760q^{35} - 8640q^{36} + 6264q^{41} + 7040q^{46} + 17912q^{49} + 1296q^{51} - 1104q^{53} + 5040q^{57} + 13584q^{59} + 1152q^{60} - 12288q^{62} - 2160q^{63} - 20480q^{64} + 1152q^{66} - 3840q^{68} + 35352q^{71} + 4608q^{74} + 3168q^{75} + 6336q^{76} - 12672q^{78} - 15720q^{79} + 29160q^{81} - 26872q^{85} + 18432q^{86} + 7776q^{87} + 8192q^{88} - 18432q^{94} - 19128q^{95} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
235.1 2.82843i 5.19615 −8.00000 −10.0054 14.6969i 10.1747 22.6274i 27.0000 28.2996i
235.2 2.82843i 5.19615 −8.00000 −10.0054 14.6969i 10.1747 22.6274i 27.0000 28.2996i
235.3 2.82843i −5.19615 −8.00000 21.2806 14.6969i −81.9829 22.6274i 27.0000 60.1907i
235.4 2.82843i −5.19615 −8.00000 21.2806 14.6969i −81.9829 22.6274i 27.0000 60.1907i
235.5 2.82843i −5.19615 −8.00000 0.141718 14.6969i −89.1589 22.6274i 27.0000 0.400839i
235.6 2.82843i −5.19615 −8.00000 0.141718 14.6969i −89.1589 22.6274i 27.0000 0.400839i
235.7 2.82843i −5.19615 −8.00000 −8.58312 14.6969i 95.1629 22.6274i 27.0000 24.2767i
235.8 2.82843i −5.19615 −8.00000 −8.58312 14.6969i 95.1629 22.6274i 27.0000 24.2767i
235.9 2.82843i −5.19615 −8.00000 −44.0140 14.6969i 46.8163 22.6274i 27.0000 124.490i
235.10 2.82843i −5.19615 −8.00000 −44.0140 14.6969i 46.8163 22.6274i 27.0000 124.490i
235.11 2.82843i −5.19615 −8.00000 0.345303 14.6969i 29.1133 22.6274i 27.0000 0.976665i
235.12 2.82843i −5.19615 −8.00000 0.345303 14.6969i 29.1133 22.6274i 27.0000 0.976665i
235.13 2.82843i 5.19615 −8.00000 −17.0264 14.6969i 47.1245 22.6274i 27.0000 48.1580i
235.14 2.82843i 5.19615 −8.00000 −17.0264 14.6969i 47.1245 22.6274i 27.0000 48.1580i
235.15 2.82843i −5.19615 −8.00000 −27.9908 14.6969i −34.1747 22.6274i 27.0000 79.1699i
235.16 2.82843i −5.19615 −8.00000 −27.9908 14.6969i −34.1747 22.6274i 27.0000 79.1699i
235.17 2.82843i 5.19615 −8.00000 −4.63644 14.6969i −33.3282 22.6274i 27.0000 13.1138i
235.18 2.82843i 5.19615 −8.00000 −4.63644 14.6969i −33.3282 22.6274i 27.0000 13.1138i
235.19 2.82843i 5.19615 −8.00000 26.1412 14.6969i −51.7193 22.6274i 27.0000 73.9384i
235.20 2.82843i 5.19615 −8.00000 26.1412 14.6969i −51.7193 22.6274i 27.0000 73.9384i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 235.40
Significant digits:
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Inner twists

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

Hecke kernels

There are no other newforms in \(S_{5}^{\mathrm{new}}(354, [\chi])\).