Properties

Label 55.2.l.a
Level 55
Weight 2
Character orbit 55.l
Analytic conductor 0.439
Analytic rank 0
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 55.l (of order \(20\) and degree \(8\))

Newform invariants

Self dual: No
Analytic conductor: \(0.439177211117\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32q - 10q^{2} - 4q^{3} - 2q^{5} - 20q^{6} - 10q^{8} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 32q - 10q^{2} - 4q^{3} - 2q^{5} - 20q^{6} - 10q^{8} - 24q^{11} + 12q^{12} - 10q^{13} + 14q^{15} - 8q^{16} - 10q^{18} + 16q^{20} + 10q^{22} - 24q^{23} + 16q^{25} + 20q^{26} - 16q^{27} + 50q^{28} + 30q^{30} - 28q^{31} + 66q^{33} - 10q^{35} + 24q^{36} - 8q^{37} + 10q^{38} - 50q^{40} + 40q^{41} - 10q^{42} - 28q^{45} + 60q^{46} - 28q^{47} - 54q^{48} - 50q^{50} + 20q^{51} - 50q^{52} - 24q^{53} - 64q^{55} - 80q^{56} + 30q^{57} - 50q^{58} + 34q^{60} - 60q^{61} + 100q^{62} - 30q^{63} - 100q^{66} - 8q^{67} - 30q^{68} + 30q^{70} + 24q^{71} + 80q^{72} + 50q^{73} + 34q^{75} + 70q^{77} + 60q^{78} + 98q^{80} - 12q^{81} - 10q^{82} + 90q^{83} + 30q^{85} + 100q^{86} + 170q^{88} - 20q^{90} + 20q^{91} - 68q^{92} - 8q^{93} - 40q^{95} - 8q^{97} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −1.15100 2.25897i 0.313634 1.98021i −2.60258 + 3.58214i 1.91314 + 1.15755i −4.83422 + 1.57073i −1.78576 + 0.282837i 6.07934 + 0.962874i −0.969677 0.315067i 0.412838 5.65406i
2.2 −0.474334 0.930933i −0.440550 + 2.78152i 0.533928 0.734888i 2.23541 + 0.0540419i 2.79838 0.909249i −0.543058 + 0.0860119i −3.00128 0.475357i −4.68963 1.52375i −1.01002 2.10665i
2.3 −0.261423 0.513072i 0.120415 0.760272i 0.980670 1.34978i −1.76986 + 1.36660i −0.421554 + 0.136971i 1.17850 0.186656i −2.08639 0.330452i 2.28966 + 0.743954i 1.16385 + 0.550801i
2.4 0.665529 + 1.30617i −0.130227 + 0.822224i −0.0875924 + 0.120561i −1.11862 1.93615i −1.16064 + 0.377114i −4.16343 + 0.659422i 2.68004 + 0.424477i 2.19408 + 0.712899i 1.78448 2.74968i
7.1 −2.40264 + 0.380541i −0.271495 0.532840i 3.72576 1.21057i 1.85044 + 1.25533i 0.855073 + 1.17691i 2.30033 + 1.17208i −4.15610 + 2.11764i 1.55315 2.13772i −4.92366 2.31195i
7.2 −1.22307 + 0.193716i 1.15501 + 2.26684i −0.443732 + 0.144177i −2.23029 0.160637i −1.85178 2.54876i 3.09022 + 1.57455i 2.72149 1.38667i −2.04114 + 2.80938i 2.75893 0.235572i
7.3 0.482327 0.0763931i 0.517260 + 1.01518i −1.67531 + 0.544341i 2.05331 0.885381i 0.327041 + 0.450133i −2.59854 1.32402i −1.63669 + 0.833936i 1.00032 1.37683i 0.922733 0.583903i
7.4 1.50135 0.237790i −0.361933 0.710333i 0.295389 0.0959778i −1.89470 + 1.18749i −0.712297 0.980393i 0.170602 + 0.0869260i −2.28811 + 1.16585i 1.38978 1.91287i −2.56223 + 2.23337i
8.1 −2.40264 0.380541i −0.271495 + 0.532840i 3.72576 + 1.21057i 1.85044 1.25533i 0.855073 1.17691i 2.30033 1.17208i −4.15610 2.11764i 1.55315 + 2.13772i −4.92366 + 2.31195i
8.2 −1.22307 0.193716i 1.15501 2.26684i −0.443732 0.144177i −2.23029 + 0.160637i −1.85178 + 2.54876i 3.09022 1.57455i 2.72149 + 1.38667i −2.04114 2.80938i 2.75893 + 0.235572i
8.3 0.482327 + 0.0763931i 0.517260 1.01518i −1.67531 0.544341i 2.05331 + 0.885381i 0.327041 0.450133i −2.59854 + 1.32402i −1.63669 0.833936i 1.00032 + 1.37683i 0.922733 + 0.583903i
8.4 1.50135 + 0.237790i −0.361933 + 0.710333i 0.295389 + 0.0959778i −1.89470 1.18749i −0.712297 + 0.980393i 0.170602 0.0869260i −2.28811 1.16585i 1.38978 + 1.91287i −2.56223 2.23337i
13.1 −2.25897 + 1.15100i 1.98021 + 0.313634i 2.60258 3.58214i −0.867371 + 2.06099i −4.83422 + 1.57073i 0.282837 + 1.78576i −0.962874 + 6.07934i 0.969677 + 0.315067i −0.412838 5.65406i
13.2 −0.930933 + 0.474334i −2.78152 0.440550i −0.533928 + 0.734888i −1.77672 + 1.35766i 2.79838 0.909249i 0.0860119 + 0.543058i 0.475357 3.00128i 4.68963 + 1.52375i 1.01002 2.10665i
13.3 −0.513072 + 0.261423i 0.760272 + 0.120415i −0.980670 + 1.34978i 2.23511 + 0.0653109i −0.421554 + 0.136971i −0.186656 1.17850i 0.330452 2.08639i −2.28966 0.743954i −1.16385 + 0.550801i
13.4 1.30617 0.665529i −0.822224 0.130227i 0.0875924 0.120561i −0.233059 2.22389i −1.16064 + 0.377114i 0.659422 + 4.16343i −0.424477 + 2.68004i −2.19408 0.712899i −1.78448 2.74968i
17.1 −2.25897 1.15100i 1.98021 0.313634i 2.60258 + 3.58214i −0.867371 2.06099i −4.83422 1.57073i 0.282837 1.78576i −0.962874 6.07934i 0.969677 0.315067i −0.412838 + 5.65406i
17.2 −0.930933 0.474334i −2.78152 + 0.440550i −0.533928 0.734888i −1.77672 1.35766i 2.79838 + 0.909249i 0.0860119 0.543058i 0.475357 + 3.00128i 4.68963 1.52375i 1.01002 + 2.10665i
17.3 −0.513072 0.261423i 0.760272 0.120415i −0.980670 1.34978i 2.23511 0.0653109i −0.421554 0.136971i −0.186656 + 1.17850i 0.330452 + 2.08639i −2.28966 + 0.743954i −1.16385 0.550801i
17.4 1.30617 + 0.665529i −0.822224 + 0.130227i 0.0875924 + 0.120561i −0.233059 + 2.22389i −1.16064 0.377114i 0.659422 4.16343i −0.424477 2.68004i −2.19408 + 0.712899i −1.78448 + 2.74968i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 52.4
Significant digits:
Format:

Inner twists

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

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(55, [\chi])\).