↑

Properties

Label 115.5.d.a
Level $115$
Weight $5$
Character orbit 115.d
Analytic conductor $11.888$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [115,5,Mod(91,115)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(115, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("115.91");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 115.d (of order \(2\), degree \(1\), 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: \(11.8875457546\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 12 q^{2} + 272 q^{4} - 166 q^{6} + 246 q^{8} + 896 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 12 q^{2} + 272 q^{4} - 166 q^{6} + 246 q^{8} + 896 q^{9} - 30 q^{12} + 204 q^{13} + 1208 q^{16} + 50 q^{18} - 258 q^{23} - 4356 q^{24} - 4000 q^{25} + 2586 q^{26} - 2928 q^{27} - 2274 q^{29} - 82 q^{31} + 5328 q^{32} - 750 q^{35} + 3010 q^{36} + 6044 q^{39} + 1086 q^{41} - 6204 q^{46} - 10272 q^{47} + 10022 q^{48} - 5626 q^{49} - 1500 q^{50} - 7966 q^{52} - 5906 q^{54} + 2600 q^{55} - 2778 q^{58} + 26346 q^{59} - 1290 q^{62} + 18542 q^{64} - 17060 q^{69} - 4800 q^{70} + 42486 q^{71} + 45650 q^{72} - 15336 q^{73} - 51492 q^{77} - 38338 q^{78} - 8328 q^{81} + 54326 q^{82} - 12850 q^{85} + 20332 q^{87} - 42024 q^{92} - 59428 q^{93} + 76038 q^{94} + 10800 q^{95} - 37262 q^{96} - 113244 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
91.1 −7.34406 5.90949 37.9353 − 11.1803i −43.3996 − 48.6157i −161.094 −46.0780 82.1091i
91.2 −7.34406 5.90949 37.9353 11.1803i −43.3996 48.6157i −161.094 −46.0780 − 82.1091i
91.3 −6.41480 −5.40062 25.1496 − 11.1803i 34.6439 39.9461i −58.6931 −51.8333 71.7196i
91.4 −6.41480 −5.40062 25.1496 11.1803i 34.6439 − 39.9461i −58.6931 −51.8333 − 71.7196i
91.5 −5.83518 15.5811 18.0493 − 11.1803i −90.9187 44.9289i −11.9583 161.771 65.2393i
91.6 −5.83518 15.5811 18.0493 11.1803i −90.9187 − 44.9289i −11.9583 161.771 − 65.2393i
91.7 −4.68831 −9.45649 5.98022 − 11.1803i 44.3349 28.1385i 46.9758 8.42527 52.4169i
91.8 −4.68831 −9.45649 5.98022 11.1803i 44.3349 − 28.1385i 46.9758 8.42527 − 52.4169i
91.9 −3.39557 −16.6588 −4.47013 − 11.1803i 56.5661 − 77.4058i 69.5077 196.516 37.9636i
91.10 −3.39557 −16.6588 −4.47013 11.1803i 56.5661 77.4058i 69.5077 196.516 − 37.9636i
91.11 −3.11306 8.30828 −6.30887 − 11.1803i −25.8642 6.01095i 69.4488 −11.9725 34.8050i
91.12 −3.11306 8.30828 −6.30887 11.1803i −25.8642 − 6.01095i 69.4488 −11.9725 − 34.8050i
91.13 −1.17931 −3.23146 −14.6092 − 11.1803i 3.81090 − 21.2126i 36.0979 −70.5577 13.1851i
91.14 −1.17931 −3.23146 −14.6092 11.1803i 3.81090 21.2126i 36.0979 −70.5577 − 13.1851i
91.15 −0.753970 13.3391 −15.4315 − 11.1803i −10.0573 4.37200i 23.6984 96.9319 8.42964i
91.16 −0.753970 13.3391 −15.4315 11.1803i −10.0573 − 4.37200i 23.6984 96.9319 − 8.42964i
91.17 2.18924 6.68855 −11.2072 − 11.1803i 14.6428 94.1703i −59.5631 −36.2633 − 24.4764i
91.18 2.18924 6.68855 −11.2072 11.1803i 14.6428 − 94.1703i −59.5631 −36.2633 24.4764i
91.19 2.62865 4.08866 −9.09019 − 11.1803i 10.7477 − 56.7651i −65.9534 −64.2829 − 29.3892i
91.20 2.62865 4.08866 −9.09019 11.1803i 10.7477 56.7651i −65.9534 −64.2829 29.3892i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 91.32
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 115.5.d.a ✓ 32
23.b odd 2 1 inner 115.5.d.a ✓ 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
115.5.d.a ✓ 32 1.a even 1 1 trivial
115.5.d.a ✓ 32 23.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(115, [\chi])\).