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Properties

Label 151.14.a.b
Level $151$
Weight $14$
Character orbit 151.a
Self dual yes
Analytic conductor $161.919$
Analytic rank $0$
Dimension $85$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [151,14,Mod(1,151)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("151.1"); S:= CuspForms(chi, 14); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(151, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 14, names="a")
 
Level: \( N \) \(=\) \( 151 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 151.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [85] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(161.918702717\)
Analytic rank: \(0\)
Dimension: \(85\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 85 q + 192 q^{2} + 1457 q^{3} + 364544 q^{4} + 187499 q^{5} + 476544 q^{6} + 473117 q^{7} + 1820859 q^{8} + 52163790 q^{9} + 3759345 q^{10} + 19713863 q^{11} + 22681461 q^{12} + 48790877 q^{13} + 126179076 q^{14}+ \cdots - 29282268288808 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −172.782 681.431 21661.8 −15060.7 −117739. −455458. −2.32734e6 −1.12997e6 2.60223e6
1.2 −172.344 −2067.34 21510.5 −49777.1 356293. −475443. −2.29536e6 2.67956e6 8.57879e6
1.3 −168.489 1425.03 20196.6 −14556.5 −240103. −124468. −2.02264e6 436396. 2.45261e6
1.4 −168.459 1841.36 20186.3 3710.65 −310194. 288319. −2.02055e6 1.79630e6 −625090.
1.5 −167.176 96.5469 19755.9 19333.2 −16140.3 555915. −1.93321e6 −1.58500e6 −3.23206e6
1.6 −167.004 2088.22 19698.2 60860.6 −348739. −487095. −1.92157e6 2.76632e6 −1.01639e7
1.7 −165.107 −2420.11 19068.2 13201.9 399576. 505499. −1.79573e6 4.26262e6 −2.17972e6
1.8 −152.500 −1611.38 15064.1 −28564.8 245735. 55362.7 −1.04800e6 1.00224e6 4.35612e6
1.9 −149.172 −2103.63 14060.2 55794.4 313802. −349286. −875364. 2.83094e6 −8.32294e6
1.10 −148.975 −668.692 14001.5 −15994.2 99618.3 −136073. −865475. −1.14717e6 2.38273e6
1.11 −145.245 655.046 12904.0 28709.1 −95142.0 −209678. −684399. −1.16524e6 −4.16985e6
1.12 −143.651 −1574.00 12443.6 26617.1 226107. 271024. −610744. 883166. −3.82357e6
1.13 −140.901 56.3191 11661.1 −63335.4 −7935.42 −267900. −488803. −1.59115e6 8.92403e6
1.14 −128.623 597.789 8351.97 −35473.0 −76889.6 226961. −20575.5 −1.23697e6 4.56266e6
1.15 −126.284 536.712 7755.63 −28616.8 −67778.1 600411. 55106.7 −1.30626e6 3.61384e6
1.16 −123.056 1611.88 6950.70 20239.7 −198351. −420102. 152749. 1.00382e6 −2.49060e6
1.17 −119.318 −1391.00 6044.77 51062.7 165971. 389205. 256203. 340549. −6.09270e6
1.18 −117.211 1096.36 5546.51 44554.2 −128506. −241089. 310082. −392320. −5.22226e6
1.19 −110.001 2320.13 3908.22 2099.38 −255217. 548239. 471220. 3.78870e6 −230934.
1.20 −108.738 −906.254 3632.04 27575.5 98544.6 308956. 495842. −773027. −2.99852e6
See all 85 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.85
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(151\) \( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 151.14.a.b ✓ 85
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
151.14.a.b ✓ 85 1.a even 1 1 trivial