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Properties

Label 925.2.bb.e
Level $925$
Weight $2$
Character orbit 925.bb
Analytic conductor $7.386$
Analytic rank $0$
Dimension $96$
Inner twists $4$

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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] = [925,2,Mod(151,925)] 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("925.151"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 13])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 925 = 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 925.bb (of order \(18\), degree \(6\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.38616218697\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(16\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 185)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
151.1 −1.72122 + 2.05127i −1.73048 + 1.45204i −0.897813 − 5.09175i 0 − 6.04896i 1.26851 + 0.461702i 7.35191 + 4.24463i 0.365177 − 2.07102i 0
151.2 −1.34451 + 1.60232i 1.31302 − 1.10176i −0.412438 − 2.33905i 0 3.58520i 3.03192 + 1.10353i 0.679545 + 0.392335i −0.0107848 + 0.0611636i 0
151.3 −1.33394 + 1.58972i −0.293922 + 0.246630i −0.400539 − 2.27157i 0 − 0.796243i −3.20026 − 1.16480i 0.551046 + 0.318147i −0.495381 + 2.80944i 0
151.4 −1.07021 + 1.27542i −1.97419 + 1.65654i −0.134064 − 0.760312i 0 − 4.29076i −0.133008 − 0.0484108i −1.77057 − 1.02224i 0.632347 − 3.58622i 0
151.5 −0.829326 + 0.988352i −0.303732 + 0.254862i 0.0582378 + 0.330283i 0 − 0.511558i −0.177770 − 0.0647030i −2.60943 − 1.50656i −0.493646 + 2.79960i 0
151.6 −0.714635 + 0.851669i 2.29252 − 1.92365i 0.132659 + 0.752349i 0 3.32718i −4.38165 − 1.59479i −2.66121 − 1.53645i 1.03426 − 5.86559i 0
151.7 −0.228808 + 0.272682i 1.77101 − 1.48605i 0.325294 + 1.84483i 0 0.822942i 0.905069 + 0.329418i −1.19403 − 0.689371i 0.407172 − 2.30919i 0
151.8 −0.0225922 + 0.0269243i −0.589240 + 0.494431i 0.347082 + 1.96840i 0 − 0.0270352i −1.90180 − 0.692199i −0.121716 − 0.0702726i −0.418203 + 2.37175i 0
151.9 0.0225922 − 0.0269243i 0.589240 − 0.494431i 0.347082 + 1.96840i 0 − 0.0270352i 1.90180 + 0.692199i 0.121716 + 0.0702726i −0.418203 + 2.37175i 0
151.10 0.228808 − 0.272682i −1.77101 + 1.48605i 0.325294 + 1.84483i 0 0.822942i −0.905069 − 0.329418i 1.19403 + 0.689371i 0.407172 − 2.30919i 0
151.11 0.714635 − 0.851669i −2.29252 + 1.92365i 0.132659 + 0.752349i 0 3.32718i 4.38165 + 1.59479i 2.66121 + 1.53645i 1.03426 − 5.86559i 0
151.12 0.829326 − 0.988352i 0.303732 − 0.254862i 0.0582378 + 0.330283i 0 − 0.511558i 0.177770 + 0.0647030i 2.60943 + 1.50656i −0.493646 + 2.79960i 0
151.13 1.07021 − 1.27542i 1.97419 − 1.65654i −0.134064 − 0.760312i 0 − 4.29076i 0.133008 + 0.0484108i 1.77057 + 1.02224i 0.632347 − 3.58622i 0
151.14 1.33394 − 1.58972i 0.293922 − 0.246630i −0.400539 − 2.27157i 0 − 0.796243i 3.20026 + 1.16480i −0.551046 − 0.318147i −0.495381 + 2.80944i 0
151.15 1.34451 − 1.60232i −1.31302 + 1.10176i −0.412438 − 2.33905i 0 3.58520i −3.03192 − 1.10353i −0.679545 − 0.392335i −0.0107848 + 0.0611636i 0
151.16 1.72122 − 2.05127i 1.73048 − 1.45204i −0.897813 − 5.09175i 0 − 6.04896i −1.26851 − 0.461702i −7.35191 − 4.24463i 0.365177 − 2.07102i 0
176.1 −2.43972 + 0.430188i −0.198906 + 1.12805i 3.88777 − 1.41503i 0 − 2.83769i −2.28969 − 1.92128i −4.58542 + 2.64739i 1.58614 + 0.577309i 0
176.2 −2.40815 + 0.424622i 0.345229 − 1.95789i 3.73949 − 1.36106i 0 4.86149i 0.316914 + 0.265922i −4.19194 + 2.42022i −0.895083 − 0.325783i 0
176.3 −2.22054 + 0.391541i −0.457886 + 2.59680i 2.89811 − 1.05483i 0 − 5.94558i 0.761600 + 0.639059i −2.11694 + 1.22222i −3.71464 − 1.35202i 0
176.4 −1.64794 + 0.290576i 0.130480 − 0.739987i 0.751873 − 0.273659i 0 1.25737i 3.79805 + 3.18694i 1.73882 − 1.00391i 2.28852 + 0.832954i 0
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 151.16
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
37.h even 18 1 inner
185.v even 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 925.2.bb.e 96
5.b even 2 1 inner 925.2.bb.e 96
5.c odd 4 2 185.2.v.a ✓ 96
37.h even 18 1 inner 925.2.bb.e 96
185.v even 18 1 inner 925.2.bb.e 96
185.y odd 36 2 185.2.v.a ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
185.2.v.a ✓ 96 5.c odd 4 2
185.2.v.a ✓ 96 185.y odd 36 2
925.2.bb.e 96 1.a even 1 1 trivial
925.2.bb.e 96 5.b even 2 1 inner
925.2.bb.e 96 37.h even 18 1 inner
925.2.bb.e 96 185.v even 18 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{96} - 6 T_{2}^{94} + 9 T_{2}^{92} - 527 T_{2}^{90} + 2775 T_{2}^{88} + 375 T_{2}^{86} + 177923 T_{2}^{84} + \cdots + 1 \) acting on \(S_{2}^{\mathrm{new}}(925, [\chi])\). Copy content Toggle raw display