Properties

Label 925.2.bn.c
Level $925$
Weight $2$
Character orbit 925.bn
Analytic conductor $7.386$
Analytic rank $0$
Dimension $312$
Inner twists $4$

Related objects

Downloads

Learn more

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(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 = [312] 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: \(312\)
Relative dimension: \(26\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 312 q + 48 q^{14} - 60 q^{16} + 24 q^{19} - 36 q^{21} + 12 q^{29} - 24 q^{31} - 60 q^{34} - 12 q^{39} + 48 q^{41} + 120 q^{44} + 24 q^{49} + 120 q^{51} - 12 q^{54} + 96 q^{56} - 48 q^{61} - 240 q^{64} - 432 q^{66}+ \cdots - 648 q^{99}+O(q^{100}) \) 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 −2.11166 − 1.77190i 0.238280 − 2.72355i 0.972210 + 5.51368i 0 −5.32902 + 5.32902i −4.12853 + 1.92516i 4.96010 − 8.59115i −4.40654 − 0.776992i 0
18.2 −1.86650 − 1.56618i 0.175688 − 2.00812i 0.683610 + 3.87694i 0 −3.47300 + 3.47300i 0.850256 − 0.396481i 2.35949 − 4.08676i −1.04726 − 0.184659i 0
18.3 −1.80675 − 1.51604i −0.226240 + 2.58593i 0.618660 + 3.50859i 0 4.32913 − 4.32913i −1.09756 + 0.511800i 1.84287 − 3.19195i −3.68142 − 0.649134i 0
18.4 −1.67977 − 1.40949i −0.192411 + 2.19926i 0.487657 + 2.76564i 0 3.42306 − 3.42306i −3.94621 + 1.84015i 0.886219 − 1.53498i −1.84532 − 0.325379i 0
18.5 −1.66073 − 1.39352i −0.141363 + 1.61579i 0.468833 + 2.65888i 0 2.48639 − 2.48639i 3.80267 − 1.77321i 0.758666 − 1.31405i 0.363632 + 0.0641181i 0
18.6 −1.45649 − 1.22214i −0.0363580 + 0.415574i 0.280440 + 1.59046i 0 0.560845 − 0.560845i −0.0364787 + 0.0170103i −0.366010 + 0.633948i 2.78304 + 0.490726i 0
18.7 −1.29439 − 1.08613i 0.136034 − 1.55487i 0.148491 + 0.842137i 0 −1.86487 + 1.86487i 0.452483 − 0.210996i −0.967252 + 1.67533i 0.555304 + 0.0979151i 0
18.8 −1.08830 − 0.913192i 0.109154 − 1.24764i 0.00318071 + 0.0180387i 0 −1.25813 + 1.25813i −1.33823 + 0.624025i −1.40766 + 2.43814i 1.40974 + 0.248575i 0
18.9 −0.688618 − 0.577820i −0.0201031 + 0.229780i −0.206976 − 1.17382i 0 0.146615 − 0.146615i −3.93989 + 1.83720i −1.43466 + 2.48490i 2.90203 + 0.511706i 0
18.10 −0.583354 − 0.489492i −0.221041 + 2.52651i −0.246597 − 1.39852i 0 1.36566 − 1.36566i 3.80585 − 1.77470i −1.30223 + 2.25552i −3.37999 − 0.595984i 0
18.11 −0.305840 − 0.256630i 0.271716 − 3.10573i −0.319617 − 1.81264i 0 −0.880124 + 0.880124i 3.61479 − 1.68561i −0.766671 + 1.32791i −6.61729 − 1.16681i 0
18.12 −0.205416 − 0.172365i −0.224177 + 2.56236i −0.334810 − 1.89880i 0 0.487710 − 0.487710i 0.739628 − 0.344894i −0.526663 + 0.912208i −3.56101 − 0.627901i 0
18.13 −0.0132305 − 0.0111017i −0.0408791 + 0.467251i −0.347245 − 1.96932i 0 0.00572811 − 0.00572811i −3.11286 + 1.45155i −0.0345397 + 0.0598245i 2.73777 + 0.482743i 0
18.14 0.0132305 + 0.0111017i 0.0408791 − 0.467251i −0.347245 − 1.96932i 0 0.00572811 − 0.00572811i 3.11286 − 1.45155i 0.0345397 − 0.0598245i 2.73777 + 0.482743i 0
18.15 0.205416 + 0.172365i 0.224177 − 2.56236i −0.334810 − 1.89880i 0 0.487710 − 0.487710i −0.739628 + 0.344894i 0.526663 − 0.912208i −3.56101 − 0.627901i 0
18.16 0.305840 + 0.256630i −0.271716 + 3.10573i −0.319617 − 1.81264i 0 −0.880124 + 0.880124i −3.61479 + 1.68561i 0.766671 − 1.32791i −6.61729 − 1.16681i 0
18.17 0.583354 + 0.489492i 0.221041 − 2.52651i −0.246597 − 1.39852i 0 1.36566 − 1.36566i −3.80585 + 1.77470i 1.30223 − 2.25552i −3.37999 − 0.595984i 0
18.18 0.688618 + 0.577820i 0.0201031 − 0.229780i −0.206976 − 1.17382i 0 0.146615 − 0.146615i 3.93989 − 1.83720i 1.43466 − 2.48490i 2.90203 + 0.511706i 0
18.19 1.08830 + 0.913192i −0.109154 + 1.24764i 0.00318071 + 0.0180387i 0 −1.25813 + 1.25813i 1.33823 − 0.624025i 1.40766 − 2.43814i 1.40974 + 0.248575i 0
18.20 1.29439 + 1.08613i −0.136034 + 1.55487i 0.148491 + 0.842137i 0 −1.86487 + 1.86487i −0.452483 + 0.210996i 0.967252 − 1.67533i 0.555304 + 0.0979151i 0
See next 80 embeddings (of 312 total)
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 18.26
Significant digits:
Format:

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.c ✓ 312
5.b even 2 1 inner 925.2.bn.c ✓ 312
5.c odd 4 2 925.2.bq.c yes 312
37.i odd 36 1 925.2.bq.c yes 312
185.z even 36 1 inner 925.2.bn.c ✓ 312
185.ba odd 36 1 925.2.bq.c yes 312
185.bc even 36 1 inner 925.2.bn.c ✓ 312
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
925.2.bn.c ✓ 312 1.a even 1 1 trivial
925.2.bn.c ✓ 312 5.b even 2 1 inner
925.2.bn.c ✓ 312 185.z even 36 1 inner
925.2.bn.c ✓ 312 185.bc even 36 1 inner
925.2.bq.c yes 312 5.c odd 4 2
925.2.bq.c yes 312 37.i odd 36 1
925.2.bq.c yes 312 185.ba odd 36 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{312} + 15 T_{2}^{308} + 2408 T_{2}^{306} + 1665 T_{2}^{304} + 48264 T_{2}^{302} + \cdots + 10\!\cdots\!41 \) acting on \(S_{2}^{\mathrm{new}}(925, [\chi])\). Copy content Toggle raw display