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Properties

Label 2151.2.b.a
Level $2151$
Weight $2$
Character orbit 2151.b
Analytic conductor $17.176$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2151.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.1758214748\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 80q - 80q^{4} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 80q - 80q^{4} + 16q^{10} + 56q^{16} + 40q^{22} - 64q^{25} - 8q^{31} + 32q^{34} - 24q^{40} - 104q^{49} - 24q^{55} + 56q^{58} + 40q^{61} - 80q^{64} - 8q^{67} - 8q^{85} - 120q^{88} + 32q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2150.1 − 2.75120i 0 −5.56908 − 1.21173i 0 − 4.92033i 9.81922i 0 −3.33371
2150.2 − 2.75120i 0 −5.56908 − 1.21173i 0 4.92033i 9.81922i 0 −3.33371
2150.3 − 2.56329i 0 −4.57046 − 2.12793i 0 − 2.62545i 6.58884i 0 −5.45450
2150.4 − 2.56329i 0 −4.57046 − 2.12793i 0 2.62545i 6.58884i 0 −5.45450
2150.5 − 2.54042i 0 −4.45371 2.74390i 0 − 3.15846i 6.23344i 0 6.97064
2150.6 − 2.54042i 0 −4.45371 2.74390i 0 3.15846i 6.23344i 0 6.97064
2150.7 − 2.53879i 0 −4.44547 1.00261i 0 − 0.202697i 6.20855i 0 2.54543
2150.8 − 2.53879i 0 −4.44547 1.00261i 0 0.202697i 6.20855i 0 2.54543
2150.9 − 2.23937i 0 −3.01478 3.12574i 0 − 3.32975i 2.27247i 0 6.99969
2150.10 − 2.23937i 0 −3.01478 3.12574i 0 3.32975i 2.27247i 0 6.99969
2150.11 − 2.14709i 0 −2.61000 2.81441i 0 − 1.25298i 1.30973i 0 6.04279
2150.12 − 2.14709i 0 −2.61000 2.81441i 0 1.25298i 1.30973i 0 6.04279
2150.13 − 2.04427i 0 −2.17903 − 3.47846i 0 − 3.44491i 0.365980i 0 −7.11089
2150.14 − 2.04427i 0 −2.17903 − 3.47846i 0 3.44491i 0.365980i 0 −7.11089
2150.15 − 1.83893i 0 −1.38165 − 0.488895i 0 − 1.94727i − 1.13709i 0 −0.899043
2150.16 − 1.83893i 0 −1.38165 − 0.488895i 0 1.94727i − 1.13709i 0 −0.899043
2150.17 − 1.79525i 0 −1.22293 − 1.07382i 0 − 2.61327i − 1.39503i 0 −1.92778
2150.18 − 1.79525i 0 −1.22293 − 1.07382i 0 2.61327i − 1.39503i 0 −1.92778
2150.19 − 1.73293i 0 −1.00304 − 1.48937i 0 − 1.62864i − 1.72766i 0 −2.58096
2150.20 − 1.73293i 0 −1.00304 − 1.48937i 0 1.62864i − 1.72766i 0 −2.58096
See all 80 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2150.80
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
239.b odd 2 1 inner
717.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2151.2.b.a ✓ 80
3.b odd 2 1 inner 2151.2.b.a ✓ 80
239.b odd 2 1 inner 2151.2.b.a ✓ 80
717.b even 2 1 inner 2151.2.b.a ✓ 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2151.2.b.a ✓ 80 1.a even 1 1 trivial
2151.2.b.a ✓ 80 3.b odd 2 1 inner
2151.2.b.a ✓ 80 239.b odd 2 1 inner
2151.2.b.a ✓ 80 717.b even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(2151, [\chi])\).