Properties

Label 20.11.d.d
Level 20
Weight 11
Character orbit 20.d
Analytic conductor 12.707
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 11 \)
Character orbit: \([\chi]\) = 20.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(12.7071450535\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut +\mathstrut 608q^{4} \) \(\mathstrut +\mathstrut 8280q^{5} \) \(\mathstrut -\mathstrut 19584q^{6} \) \(\mathstrut +\mathstrut 597192q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut +\mathstrut 608q^{4} \) \(\mathstrut +\mathstrut 8280q^{5} \) \(\mathstrut -\mathstrut 19584q^{6} \) \(\mathstrut +\mathstrut 597192q^{9} \) \(\mathstrut +\mathstrut 223600q^{10} \) \(\mathstrut -\mathstrut 1706016q^{14} \) \(\mathstrut -\mathstrut 4733376q^{16} \) \(\mathstrut +\mathstrut 1631520q^{20} \) \(\mathstrut -\mathstrut 13030368q^{21} \) \(\mathstrut +\mathstrut 10190784q^{24} \) \(\mathstrut +\mathstrut 8826200q^{25} \) \(\mathstrut -\mathstrut 9454368q^{26} \) \(\mathstrut +\mathstrut 121656816q^{29} \) \(\mathstrut +\mathstrut 103616160q^{30} \) \(\mathstrut -\mathstrut 335231168q^{34} \) \(\mathstrut -\mathstrut 276632160q^{36} \) \(\mathstrut -\mathstrut 559048000q^{40} \) \(\mathstrut +\mathstrut 892843248q^{41} \) \(\mathstrut +\mathstrut 766329600q^{44} \) \(\mathstrut -\mathstrut 248162040q^{45} \) \(\mathstrut +\mathstrut 433181216q^{46} \) \(\mathstrut -\mathstrut 738102008q^{49} \) \(\mathstrut +\mathstrut 765396000q^{50} \) \(\mathstrut +\mathstrut 139387968q^{54} \) \(\mathstrut -\mathstrut 2629032384q^{56} \) \(\mathstrut +\mathstrut 296160000q^{60} \) \(\mathstrut +\mathstrut 228563248q^{61} \) \(\mathstrut -\mathstrut 1875284992q^{64} \) \(\mathstrut -\mathstrut 2069145600q^{65} \) \(\mathstrut -\mathstrut 1440259200q^{66} \) \(\mathstrut -\mathstrut 943422432q^{69} \) \(\mathstrut +\mathstrut 3242642240q^{70} \) \(\mathstrut +\mathstrut 21045467232q^{74} \) \(\mathstrut +\mathstrut 828422400q^{76} \) \(\mathstrut +\mathstrut 11736799680q^{80} \) \(\mathstrut -\mathstrut 5619065544q^{81} \) \(\mathstrut -\mathstrut 28069573632q^{84} \) \(\mathstrut -\mathstrut 18119744000q^{85} \) \(\mathstrut +\mathstrut 8163556416q^{86} \) \(\mathstrut +\mathstrut 4631088816q^{89} \) \(\mathstrut -\mathstrut 16754463600q^{90} \) \(\mathstrut +\mathstrut 63404384q^{94} \) \(\mathstrut -\mathstrut 5617046784q^{96} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
19.1 −31.7400 4.07116i 190.073 990.851 + 258.437i 101.732 + 3123.34i −6032.92 773.819i 14056.7 −30397.4 12236.7i −22921.2 9486.66 99549.0i
19.2 −31.7400 + 4.07116i 190.073 990.851 258.437i 101.732 3123.34i −6032.92 + 773.819i 14056.7 −30397.4 + 12236.7i −22921.2 9486.66 + 99549.0i
19.3 −28.1904 15.1426i −349.582 565.401 + 853.755i 1690.09 2628.54i 9854.87 + 5293.59i 15402.9 −3010.79 32629.4i 63158.6 −87447.4 + 48507.3i
19.4 −28.1904 + 15.1426i −349.582 565.401 853.755i 1690.09 + 2628.54i 9854.87 5293.59i 15402.9 −3010.79 + 32629.4i 63158.6 −87447.4 48507.3i
19.5 −23.9223 21.2538i 94.4407 120.549 + 1016.88i 3107.65 + 328.861i −2259.24 2007.23i −20081.9 18728.8 26888.2i −50129.9 −67352.4 73916.5i
19.6 −23.9223 + 21.2538i 94.4407 120.549 1016.88i 3107.65 328.861i −2259.24 + 2007.23i −20081.9 18728.8 + 26888.2i −50129.9 −67352.4 + 73916.5i
19.7 −21.8278 23.3997i 416.738 −71.0958 + 1021.53i −2532.23 1831.23i −9096.47 9751.56i −9550.48 25455.4 20634.1i 114622. 12422.7 + 99225.4i
19.8 −21.8278 + 23.3997i 416.738 −71.0958 1021.53i −2532.23 + 1831.23i −9096.47 + 9751.56i −9550.48 25455.4 + 20634.1i 114622. 12422.7 99225.4i
19.9 −17.2353 26.9619i −146.443 −429.889 + 929.393i −2538.13 + 1823.05i 2523.99 + 3948.38i 13979.7 32467.5 4427.76i −37603.5 92898.4 + 37012.0i
19.10 −17.2353 + 26.9619i −146.443 −429.889 929.393i −2538.13 1823.05i 2523.99 3948.38i 13979.7 32467.5 + 4427.76i −37603.5 92898.4 37012.0i
19.11 −0.302723 31.9986i −375.794 −1023.82 + 19.3734i 2240.90 + 2178.07i 113.762 + 12024.9i −19635.7 929.854 + 32754.8i 82172.5 69016.9 72364.8i
19.12 −0.302723 + 31.9986i −375.794 −1023.82 19.3734i 2240.90 2178.07i 113.762 12024.9i −19635.7 929.854 32754.8i 82172.5 69016.9 + 72364.8i
19.13 0.302723 31.9986i 375.794 −1023.82 19.3734i 2240.90 + 2178.07i 113.762 12024.9i 19635.7 −929.854 + 32754.8i 82172.5 70373.6 71046.1i
19.14 0.302723 + 31.9986i 375.794 −1023.82 + 19.3734i 2240.90 2178.07i 113.762 + 12024.9i 19635.7 −929.854 32754.8i 82172.5 70373.6 + 71046.1i
19.15 17.2353 26.9619i 146.443 −429.889 929.393i −2538.13 + 1823.05i 2523.99 3948.38i −13979.7 −32467.5 4427.76i −37603.5 5407.52 + 99853.7i
19.16 17.2353 + 26.9619i 146.443 −429.889 + 929.393i −2538.13 1823.05i 2523.99 + 3948.38i −13979.7 −32467.5 + 4427.76i −37603.5 5407.52 99853.7i
19.17 21.8278 23.3997i −416.738 −71.0958 1021.53i −2532.23 1831.23i −9096.47 + 9751.56i 9550.48 −25455.4 20634.1i 114622. −98123.4 + 19281.8i
19.18 21.8278 + 23.3997i −416.738 −71.0958 + 1021.53i −2532.23 + 1831.23i −9096.47 9751.56i 9550.48 −25455.4 + 20634.1i 114622. −98123.4 19281.8i
19.19 23.9223 21.2538i −94.4407 120.549 1016.88i 3107.65 + 328.861i −2259.24 + 2007.23i 20081.9 −18728.8 26888.2i −50129.9 81331.5 58182.3i
19.20 23.9223 + 21.2538i −94.4407 120.549 + 1016.88i 3107.65 328.861i −2259.24 2007.23i 20081.9 −18728.8 + 26888.2i −50129.9 81331.5 + 58182.3i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 19.24
Significant digits:
Format:

Inner twists

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

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{12} \) \(\mathstrut -\mathstrut 503592 T_{3}^{10} \) \(\mathstrut +\mathstrut 93360281616 T_{3}^{8} \) \(\mathstrut -\mathstrut \)\(77\!\cdots\!00\)\( T_{3}^{6} \) \(\mathstrut +\mathstrut \)\(28\!\cdots\!00\)\( T_{3}^{4} \) \(\mathstrut -\mathstrut \)\(42\!\cdots\!00\)\( T_{3}^{2} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!00\)\( \) acting on \(S_{11}^{\mathrm{new}}(20, [\chi])\).