Properties

Label 150.2.l.a
Level 150
Weight 2
Character orbit 150.l
Analytic conductor 1.198
Analytic rank 0
Dimension 80
CM No

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Newspace parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 150.l (of order \(20\) and degree \(8\))

Newform invariants

Self dual: No
Analytic conductor: \(1.19775603032\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) 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.

\(\operatorname{Tr}(f)(q) = \) \(80q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(80q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 8q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 104q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut +\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 40q^{34} \) \(\mathstrut -\mathstrut 24q^{37} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut -\mathstrut 72q^{45} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut +\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 64q^{63} \) \(\mathstrut +\mathstrut 96q^{67} \) \(\mathstrut +\mathstrut 140q^{69} \) \(\mathstrut +\mathstrut 76q^{70} \) \(\mathstrut +\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 100q^{73} \) \(\mathstrut +\mathstrut 132q^{75} \) \(\mathstrut +\mathstrut 100q^{78} \) \(\mathstrut +\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 40q^{81} \) \(\mathstrut +\mathstrut 96q^{82} \) \(\mathstrut +\mathstrut 60q^{84} \) \(\mathstrut +\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 80q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 52q^{90} \) \(\mathstrut +\mathstrut 12q^{93} \) \(\mathstrut -\mathstrut 32q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 −0.891007 0.453990i −1.64867 0.530925i 0.587785 + 0.809017i 1.35266 + 1.78054i 1.22794 + 1.22154i −0.152718 0.152718i −0.156434 0.987688i 2.43624 + 1.75064i −0.396880 2.20056i
17.2 −0.891007 0.453990i −0.873670 + 1.49556i 0.587785 + 0.809017i −2.21391 + 0.314018i 1.45742 0.935916i −2.72680 2.72680i −0.156434 0.987688i −1.47340 2.61325i 2.11517 + 0.725301i
17.3 −0.891007 0.453990i −0.322239 1.70181i 0.587785 + 0.809017i −0.0831552 2.23452i −0.485490 + 1.66262i 0.0556476 + 0.0556476i −0.156434 0.987688i −2.79232 + 1.09678i −0.940360 + 2.02872i
17.4 −0.891007 0.453990i 0.983013 + 1.42607i 0.587785 + 0.809017i 1.04600 1.97633i −0.228447 1.71692i 0.462249 + 0.462249i −0.156434 0.987688i −1.06737 + 2.80370i −1.82923 + 1.28605i
17.5 −0.891007 0.453990i 1.71953 + 0.207905i 0.587785 + 0.809017i −1.62298 + 1.53816i −1.43772 0.965894i 2.58285 + 2.58285i −0.156434 0.987688i 2.91355 + 0.714995i 2.14440 0.633691i
17.6 0.891007 + 0.453990i −1.69961 0.333634i 0.587785 + 0.809017i 1.62298 1.53816i −1.36290 1.06888i 2.58285 + 2.58285i 0.156434 + 0.987688i 2.77738 + 1.13410i 2.14440 0.633691i
17.7 0.891007 + 0.453990i −1.37558 + 1.05251i 0.587785 + 0.809017i −1.04600 + 1.97633i −1.70348 + 0.313291i 0.462249 + 0.462249i 0.156434 + 0.987688i 0.784450 2.89562i −1.82923 + 1.28605i
17.8 0.891007 + 0.453990i 0.368756 + 1.69234i 0.587785 + 0.809017i 2.21391 0.314018i −0.439743 + 1.67530i −2.72680 2.72680i 0.156434 + 0.987688i −2.72804 + 1.24812i 2.11517 + 0.725301i
17.9 0.891007 + 0.453990i 0.832356 1.51894i 0.587785 + 0.809017i 0.0831552 + 2.23452i 1.43122 0.975505i 0.0556476 + 0.0556476i 0.156434 + 0.987688i −1.61437 2.52860i −0.940360 + 2.02872i
17.10 0.891007 + 0.453990i 1.73204 + 0.00452789i 0.587785 + 0.809017i −1.35266 1.78054i 1.54121 + 0.790366i −0.152718 0.152718i 0.156434 + 0.987688i 2.99996 + 0.0156850i −0.396880 2.20056i
23.1 −0.987688 0.156434i −1.58737 + 0.693000i 0.951057 + 0.309017i −0.197931 2.22729i 1.67624 0.436149i −1.43195 + 1.43195i −0.891007 0.453990i 2.03950 2.20010i −0.152931 + 2.23083i
23.2 −0.987688 0.156434i −1.36724 1.06332i 0.951057 + 0.309017i −1.48885 + 1.66833i 1.18407 + 1.26411i −1.08662 + 1.08662i −0.891007 0.453990i 0.738706 + 2.90763i 1.73150 1.41488i
23.3 −0.987688 0.156434i 0.487767 1.66195i 0.951057 + 0.309017i 2.22772 0.193062i −0.741748 + 1.56519i −0.104631 + 0.104631i −0.891007 0.453990i −2.52417 1.62129i −2.23049 0.157807i
23.4 −0.987688 0.156434i 1.10553 + 1.33334i 0.951057 + 0.309017i −0.334535 2.21090i −0.883341 1.48987i 2.78015 2.78015i −0.891007 0.453990i −0.555594 + 2.94810i −0.0154450 + 2.23601i
23.5 −0.987688 0.156434i 1.64008 + 0.556890i 0.951057 + 0.309017i 0.545143 + 2.16860i −1.53277 0.806599i −1.41702 + 1.41702i −0.891007 0.453990i 2.37975 + 1.82669i −0.199188 2.22718i
23.6 0.987688 + 0.156434i −1.49368 + 0.876876i 0.951057 + 0.309017i 0.197931 + 2.22729i −1.61247 + 0.632416i −1.43195 + 1.43195i 0.891007 + 0.453990i 1.46218 2.61955i −0.152931 + 2.23083i
23.7 0.987688 + 0.156434i −0.428879 1.67811i 0.951057 + 0.309017i 0.334535 + 2.21090i −0.161084 1.72454i 2.78015 2.78015i 0.891007 + 0.453990i −2.63213 + 1.43942i −0.0154450 + 2.23601i
23.8 0.987688 + 0.156434i 0.0565979 + 1.73113i 0.951057 + 0.309017i 1.48885 1.66833i −0.214907 + 1.71867i −1.08662 + 1.08662i 0.891007 + 0.453990i −2.99359 + 0.195956i 1.73150 1.41488i
23.9 0.987688 + 0.156434i 0.513483 1.65419i 0.951057 + 0.309017i −0.545143 2.16860i 0.765933 1.55349i −1.41702 + 1.41702i 0.891007 + 0.453990i −2.47267 1.69880i −0.199188 2.22718i
23.10 0.987688 + 0.156434i 1.63125 + 0.582259i 0.951057 + 0.309017i −2.22772 + 0.193062i 1.52008 + 0.830274i −0.104631 + 0.104631i 0.891007 + 0.453990i 2.32195 + 1.89962i −2.23049 0.157807i
See all 80 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 137.10
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 \(S_{2}^{\mathrm{new}}(150, [\chi])\).