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Properties

Label 151.12.a.b
Level $151$
Weight $12$
Character orbit 151.a
Self dual yes
Analytic conductor $116.020$
Analytic rank $0$
Dimension $72$
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] = [151,12,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, 12); 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, 12, names="a")
 
Level: \( N \) \(=\) \( 151 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 151.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [72] 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: \(116.019820264\)
Analytic rank: \(0\)
Dimension: \(72\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 72 q + 96 q^{2} + 719 q^{3} + 76800 q^{4} + 32669 q^{5} + 62208 q^{6} + 48045 q^{7} + 332331 q^{8} + 5218827 q^{9} + 326849 q^{10} + 1825499 q^{11} + 2261853 q^{12} + 1312687 q^{13} + 8226356 q^{14} + 613376 q^{15}+ \cdots + 723642496724 q^{99}+O(q^{100}) \) 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 −89.9616 808.499 6045.09 −358.907 −72733.9 −33454.6 −359584. 476524. 32287.9
1.2 −83.5075 −525.176 4925.51 13315.3 43856.2 86945.4 −240294. 98663.3 −1.11192e6
1.3 −82.5014 −421.865 4758.48 −293.652 34804.5 10618.2 −223619. 823.051 24226.7
1.4 −82.3202 100.575 4728.62 −9849.01 −8279.33 17209.3 −220669. −167032. 810773.
1.5 −80.0141 −829.608 4354.26 5530.12 66380.3 −47109.4 −184533. 511102. −442488.
1.6 −77.8019 520.623 4005.14 −3706.61 −40505.5 −40107.6 −152269. 93901.7 288382.
1.7 −76.7894 498.774 3848.62 −7936.48 −38300.6 −39546.7 −138268. 71629.0 609438.
1.8 −75.3434 116.967 3628.63 850.325 −8812.67 56462.4 −119090. −163466. −64066.3
1.9 −74.0388 −482.351 3433.74 9798.61 35712.7 4473.40 −102599. 55515.2 −725478.
1.10 −73.0670 672.054 3290.78 9227.96 −49105.0 50310.7 −90806.3 274510. −674259.
1.11 −72.7987 −362.956 3251.66 −4616.90 26422.7 57191.5 −87624.8 −45410.0 336104.
1.12 −65.0803 329.818 2187.45 3569.88 −21464.7 −83888.7 −9075.13 −68366.9 −232329.
1.13 −64.5200 −434.604 2114.83 −7980.10 28040.6 −69719.1 −4311.65 11733.7 514876.
1.14 −63.4312 −569.274 1975.51 −9021.34 36109.7 −54556.4 4598.06 146926. 572234.
1.15 −60.8727 −108.874 1657.49 9869.17 6627.49 −39.5040 23771.4 −165293. −600763.
1.16 −57.6592 −428.433 1276.59 7616.14 24703.1 −11186.7 44479.1 6407.54 −439141.
1.17 −50.6433 508.840 516.743 2818.50 −25769.4 27112.8 77547.9 81771.6 −142738.
1.18 −49.7129 659.406 423.374 4651.31 −32781.0 −78196.4 80764.9 257669. −231230.
1.19 −49.1864 245.619 371.299 −4297.23 −12081.1 −491.370 82470.8 −116818. 211365.
1.20 −47.0672 −210.075 167.317 10200.9 9887.65 −26383.4 88518.4 −133015. −480128.
See all 72 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.72
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 151.12.a.b ✓ 72
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
151.12.a.b ✓ 72 1.a even 1 1 trivial