Properties

Label 1890.2.bi.a
Level $1890$
Weight $2$
Character orbit 1890.bi
Analytic conductor $15.092$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1890,2,Mod(719,1890)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1890.719");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1890.bi (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(15.0917259820\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 48 q^{2} + 48 q^{4} + 3 q^{7} - 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q - 48 q^{2} + 48 q^{4} + 3 q^{7} - 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} + 6 q^{22} - 3 q^{23} - 18 q^{25} + 3 q^{28} + 3 q^{29} - 48 q^{32} + 12 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49} + 18 q^{50} - 42 q^{55} - 3 q^{56} - 3 q^{58} + 48 q^{64} - 12 q^{65} - 12 q^{70} - 18 q^{73} + 12 q^{77} - 3 q^{82} - 9 q^{83} - 33 q^{85} + 6 q^{88} + 33 q^{89} - 3 q^{92} - 24 q^{97} - 3 q^{98}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
719.1 −1.00000 0 1.00000 −2.22760 0.194363i 0 −2.20085 + 1.46842i −1.00000 0 2.22760 + 0.194363i
719.2 −1.00000 0 1.00000 −2.20530 + 0.369687i 0 2.33660 1.24108i −1.00000 0 2.20530 0.369687i
719.3 −1.00000 0 1.00000 −2.07140 0.842204i 0 −1.57200 2.12810i −1.00000 0 2.07140 + 0.842204i
719.4 −1.00000 0 1.00000 −1.98394 + 1.03150i 0 0.994947 + 2.45155i −1.00000 0 1.98394 1.03150i
719.5 −1.00000 0 1.00000 −1.67933 + 1.47644i 0 −2.41546 1.07960i −1.00000 0 1.67933 1.47644i
719.6 −1.00000 0 1.00000 −1.41134 1.73440i 0 2.55753 + 0.677517i −1.00000 0 1.41134 + 1.73440i
719.7 −1.00000 0 1.00000 −1.24107 1.86004i 0 2.20215 1.46647i −1.00000 0 1.24107 + 1.86004i
719.8 −1.00000 0 1.00000 −1.22943 + 1.86775i 0 −0.691773 + 2.55371i −1.00000 0 1.22943 1.86775i
719.9 −1.00000 0 1.00000 −0.719036 2.11731i 0 −1.31170 + 2.29771i −1.00000 0 0.719036 + 2.11731i
719.10 −1.00000 0 1.00000 −0.543458 + 2.16902i 0 −1.39638 2.24725i −1.00000 0 0.543458 2.16902i
719.11 −1.00000 0 1.00000 −0.325622 2.21223i 0 −1.75469 1.98017i −1.00000 0 0.325622 + 2.21223i
719.12 −1.00000 0 1.00000 −0.307273 + 2.21486i 0 −0.431605 2.61031i −1.00000 0 0.307273 2.21486i
719.13 −1.00000 0 1.00000 −0.0611015 2.23523i 0 1.83478 + 1.90619i −1.00000 0 0.0611015 + 2.23523i
719.14 −1.00000 0 1.00000 0.255938 + 2.22137i 0 2.61687 + 0.389830i −1.00000 0 −0.255938 2.22137i
719.15 −1.00000 0 1.00000 0.381768 + 2.20324i 0 2.63972 0.178501i −1.00000 0 −0.381768 2.20324i
719.16 −1.00000 0 1.00000 0.834189 + 2.07464i 0 −1.94702 + 1.79140i −1.00000 0 −0.834189 2.07464i
719.17 −1.00000 0 1.00000 0.930691 2.03318i 0 −2.58635 + 0.557485i −1.00000 0 −0.930691 + 2.03318i
719.18 −1.00000 0 1.00000 1.55089 1.61082i 0 −0.405354 2.61451i −1.00000 0 −1.55089 + 1.61082i
719.19 −1.00000 0 1.00000 1.71175 1.43872i 0 2.20678 + 1.45950i −1.00000 0 −1.71175 + 1.43872i
719.20 −1.00000 0 1.00000 1.93822 1.11504i 0 1.80444 1.93494i −1.00000 0 −1.93822 + 1.11504i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 719.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
315.bq even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1890.2.bi.a 48
3.b odd 2 1 630.2.bi.b yes 48
5.b even 2 1 1890.2.bi.b 48
7.d odd 6 1 1890.2.r.b 48
9.c even 3 1 630.2.r.b yes 48
9.d odd 6 1 1890.2.r.a 48
15.d odd 2 1 630.2.bi.a yes 48
21.g even 6 1 630.2.r.a 48
35.i odd 6 1 1890.2.r.a 48
45.h odd 6 1 1890.2.r.b 48
45.j even 6 1 630.2.r.a 48
63.i even 6 1 1890.2.bi.b 48
63.t odd 6 1 630.2.bi.a yes 48
105.p even 6 1 630.2.r.b yes 48
315.q odd 6 1 630.2.bi.b yes 48
315.bq even 6 1 inner 1890.2.bi.a 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
630.2.r.a 48 21.g even 6 1
630.2.r.a 48 45.j even 6 1
630.2.r.b yes 48 9.c even 3 1
630.2.r.b yes 48 105.p even 6 1
630.2.bi.a yes 48 15.d odd 2 1
630.2.bi.a yes 48 63.t odd 6 1
630.2.bi.b yes 48 3.b odd 2 1
630.2.bi.b yes 48 315.q odd 6 1
1890.2.r.a 48 9.d odd 6 1
1890.2.r.a 48 35.i odd 6 1
1890.2.r.b 48 7.d odd 6 1
1890.2.r.b 48 45.h odd 6 1
1890.2.bi.a 48 1.a even 1 1 trivial
1890.2.bi.a 48 315.bq even 6 1 inner
1890.2.bi.b 48 5.b even 2 1
1890.2.bi.b 48 63.i even 6 1