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Properties

Label 1890.2.m.d
Level $1890$
Weight $2$
Character orbit 1890.m
Analytic conductor $15.092$
Analytic rank $0$
Dimension $24$
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(323,1890)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1890, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1890.323");
 
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.m (of order \(4\), degree \(2\), 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: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{5}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{5} + 24 q^{14} - 24 q^{16} + 16 q^{17} + 8 q^{22} - 8 q^{25} - 16 q^{29} - 16 q^{31} - 8 q^{35} - 16 q^{37} + 8 q^{38} + 8 q^{40} - 8 q^{43} + 8 q^{44} + 16 q^{46} + 16 q^{47} + 32 q^{50} - 24 q^{53} + 40 q^{55} + 8 q^{58} + 32 q^{59} + 40 q^{62} - 24 q^{65} - 24 q^{67} - 16 q^{68} + 8 q^{70} - 24 q^{73} - 16 q^{74} - 8 q^{77} - 8 q^{80} - 8 q^{82} + 48 q^{83} - 24 q^{85} + 8 q^{88} + 48 q^{89} + 72 q^{95} + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
323.1 −0.707107 − 0.707107i 0 1.00000i 0.490937 + 2.18151i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 1.19542 − 1.88970i
323.2 −0.707107 − 0.707107i 0 1.00000i −1.61522 − 1.54630i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 0.0487327 + 2.23554i
323.3 −0.707107 − 0.707107i 0 1.00000i 1.85011 + 1.25582i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 −0.420223 − 2.19623i
323.4 −0.707107 − 0.707107i 0 1.00000i 2.18442 − 0.477839i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 −1.88250 − 1.20673i
323.5 −0.707107 − 0.707107i 0 1.00000i 0.247475 + 2.22233i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 1.39643 − 1.74642i
323.6 −0.707107 − 0.707107i 0 1.00000i 0.256500 − 2.22131i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 −1.75207 + 1.38933i
323.7 0.707107 + 0.707107i 0 1.00000i 2.18368 + 0.481168i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 1.20386 + 1.88434i
323.8 0.707107 + 0.707107i 0 1.00000i −2.16482 + 0.559965i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 −1.92671 − 1.13480i
323.9 0.707107 + 0.707107i 0 1.00000i −2.11918 − 0.713491i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 −0.993973 − 2.00300i
323.10 0.707107 + 0.707107i 0 1.00000i 0.542742 − 2.16920i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 1.91763 − 1.15008i
323.11 0.707107 + 0.707107i 0 1.00000i 0.690225 + 2.12687i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 −1.01586 + 1.99199i
323.12 0.707107 + 0.707107i 0 1.00000i 1.45314 − 1.69953i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 2.22927 − 0.174226i
1457.1 −0.707107 + 0.707107i 0 − 1.00000i 0.490937 − 2.18151i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 1.19542 + 1.88970i
1457.2 −0.707107 + 0.707107i 0 − 1.00000i −1.61522 + 1.54630i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 0.0487327 − 2.23554i
1457.3 −0.707107 + 0.707107i 0 − 1.00000i 1.85011 − 1.25582i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 −0.420223 + 2.19623i
1457.4 −0.707107 + 0.707107i 0 − 1.00000i 2.18442 + 0.477839i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 −1.88250 + 1.20673i
1457.5 −0.707107 + 0.707107i 0 − 1.00000i 0.247475 − 2.22233i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 1.39643 + 1.74642i
1457.6 −0.707107 + 0.707107i 0 − 1.00000i 0.256500 + 2.22131i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 −1.75207 − 1.38933i
1457.7 0.707107 − 0.707107i 0 − 1.00000i 2.18368 − 0.481168i 0 0.707107 + 0.707107i −0.707107 − 0.707107i 0 1.20386 − 1.88434i
1457.8 0.707107 − 0.707107i 0 − 1.00000i −2.16482 − 0.559965i 0 0.707107 + 0.707107i −0.707107 − 0.707107i 0 −1.92671 + 1.13480i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 323.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
15.e even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1890.2.m.d yes 24
3.b odd 2 1 1890.2.m.a ✓ 24
5.c odd 4 1 1890.2.m.a ✓ 24
15.e even 4 1 inner 1890.2.m.d yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1890.2.m.a ✓ 24 3.b odd 2 1
1890.2.m.a ✓ 24 5.c odd 4 1
1890.2.m.d yes 24 1.a even 1 1 trivial
1890.2.m.d yes 24 15.e even 4 1 inner