Properties

Label 925.2.bn.a
Level $925$
Weight $2$
Character orbit 925.bn
Analytic conductor $7.386$
Analytic rank $0$
Dimension $144$
Inner twists $4$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [925,2,Mod(18,925)] 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("925.18"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([27, 17])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 925 = 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 925.bn (of order \(36\), degree \(12\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [144] 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: no
Analytic conductor: \(7.38616218697\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(12\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 144 q + 24 q^{14} + 60 q^{16} - 24 q^{19} + 36 q^{21} - 12 q^{29} - 12 q^{31} + 60 q^{34} - 60 q^{39} + 24 q^{41} + 60 q^{44} - 132 q^{49} - 120 q^{51} + 12 q^{54} - 96 q^{56} - 24 q^{61} + 12 q^{64} - 216 q^{66}+ \cdots + 72 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
18.1 −2.02165 − 1.69637i −0.0131441 + 0.150238i 0.862120 + 4.88932i 0 0.281432 − 0.281432i −0.830481 + 0.387260i 3.91211 − 6.77597i 2.93202 + 0.516995i 0
18.2 −1.63278 − 1.37006i 0.277927 − 3.17672i 0.441596 + 2.50441i 0 −4.80611 + 4.80611i 1.75134 − 0.816664i 0.578738 − 1.00240i −7.05991 − 1.24485i 0
18.3 −1.54854 − 1.29938i −0.219182 + 2.50527i 0.362289 + 2.05464i 0 3.59469 − 3.59469i 2.46980 − 1.15169i 0.0872639 − 0.151146i −3.27389 − 0.577275i 0
18.4 −1.01071 − 0.848085i −0.171623 + 1.96166i −0.0450135 − 0.255284i 0 1.83711 − 1.83711i −1.57503 + 0.734450i −1.49039 + 2.58144i −0.864232 − 0.152387i 0
18.5 −0.688403 − 0.577639i 0.0740559 − 0.846463i −0.207064 − 1.17432i 0 −0.539931 + 0.539931i 3.54162 − 1.65148i −1.43444 + 2.48451i 2.24341 + 0.395573i 0
18.6 −0.289780 − 0.243154i 0.119645 − 1.36754i −0.322448 − 1.82869i 0 −0.367195 + 0.367195i −0.852305 + 0.397436i −0.729496 + 1.26352i 1.09856 + 0.193706i 0
18.7 0.289780 + 0.243154i −0.119645 + 1.36754i −0.322448 − 1.82869i 0 −0.367195 + 0.367195i 0.852305 − 0.397436i 0.729496 − 1.26352i 1.09856 + 0.193706i 0
18.8 0.688403 + 0.577639i −0.0740559 + 0.846463i −0.207064 − 1.17432i 0 −0.539931 + 0.539931i −3.54162 + 1.65148i 1.43444 − 2.48451i 2.24341 + 0.395573i 0
18.9 1.01071 + 0.848085i 0.171623 − 1.96166i −0.0450135 − 0.255284i 0 1.83711 − 1.83711i 1.57503 − 0.734450i 1.49039 − 2.58144i −0.864232 − 0.152387i 0
18.10 1.54854 + 1.29938i 0.219182 − 2.50527i 0.362289 + 2.05464i 0 3.59469 − 3.59469i −2.46980 + 1.15169i −0.0872639 + 0.151146i −3.27389 − 0.577275i 0
18.11 1.63278 + 1.37006i −0.277927 + 3.17672i 0.441596 + 2.50441i 0 −4.80611 + 4.80611i −1.75134 + 0.816664i −0.578738 + 1.00240i −7.05991 − 1.24485i 0
18.12 2.02165 + 1.69637i 0.0131441 − 0.150238i 0.862120 + 4.88932i 0 0.281432 − 0.281432i 0.830481 − 0.387260i −3.91211 + 6.77597i 2.93202 + 0.516995i 0
143.1 −2.33789 + 0.850922i −1.48855 + 0.694124i 3.20957 − 2.69315i 0 2.88943 − 2.88943i 0.132105 + 0.0925011i −2.72402 + 4.71815i −0.194377 + 0.231650i 0
143.2 −2.11947 + 0.771426i 1.90043 − 0.886187i 2.36499 − 1.98446i 0 −3.34429 + 3.34429i −3.16976 − 2.21949i −1.22617 + 2.12379i 0.897959 − 1.07015i 0
143.3 −1.63491 + 0.595060i 1.78393 − 0.831862i 0.786759 − 0.660169i 0 −2.42157 + 2.42157i 3.37111 + 2.36047i 0.846397 − 1.46600i 0.562066 − 0.669844i 0
143.4 −1.23702 + 0.450237i −0.478168 + 0.222974i −0.204595 + 0.171675i 0 0.491111 − 0.491111i 1.85002 + 1.29540i 1.49220 − 2.58456i −1.74944 + 2.08490i 0
143.5 −1.17506 + 0.427687i −2.76987 + 1.29161i −0.334240 + 0.280461i 0 2.70236 − 2.70236i −2.70903 − 1.89689i 1.52327 − 2.63839i 4.07558 − 4.85708i 0
143.6 −0.271270 + 0.0987344i 1.40760 − 0.656375i −1.46825 + 1.23201i 0 −0.317034 + 0.317034i −1.04897 − 0.734500i 0.565331 − 0.979182i −0.377850 + 0.450304i 0
143.7 0.271270 − 0.0987344i −1.40760 + 0.656375i −1.46825 + 1.23201i 0 −0.317034 + 0.317034i 1.04897 + 0.734500i −0.565331 + 0.979182i −0.377850 + 0.450304i 0
143.8 1.17506 − 0.427687i 2.76987 − 1.29161i −0.334240 + 0.280461i 0 2.70236 − 2.70236i 2.70903 + 1.89689i −1.52327 + 2.63839i 4.07558 − 4.85708i 0
See next 80 embeddings (of 144 total)
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 18.12
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
185.z even 36 1 inner
185.bc even 36 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 925.2.bn.a ✓ 144
5.b even 2 1 inner 925.2.bn.a ✓ 144
5.c odd 4 2 925.2.bq.a yes 144
37.i odd 36 1 925.2.bq.a yes 144
185.z even 36 1 inner 925.2.bn.a ✓ 144
185.ba odd 36 1 925.2.bq.a yes 144
185.bc even 36 1 inner 925.2.bn.a ✓ 144
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
925.2.bn.a ✓ 144 1.a even 1 1 trivial
925.2.bn.a ✓ 144 5.b even 2 1 inner
925.2.bn.a ✓ 144 185.z even 36 1 inner
925.2.bn.a ✓ 144 185.bc even 36 1 inner
925.2.bq.a yes 144 5.c odd 4 2
925.2.bq.a yes 144 37.i odd 36 1
925.2.bq.a yes 144 185.ba odd 36 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{144} - 15 T_{2}^{140} + 898 T_{2}^{138} - 576 T_{2}^{136} - 17874 T_{2}^{134} + 522721 T_{2}^{132} + \cdots + 1073283121 \) acting on \(S_{2}^{\mathrm{new}}(925, [\chi])\). Copy content Toggle raw display