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Properties

Label 531.5.c.d
Level $531$
Weight $5$
Character orbit 531.c
Analytic conductor $54.889$
Analytic rank $0$
Dimension $40$
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] = [531,5,Mod(235,531)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(531, 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("531.235");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 531.c (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: \(54.8894503975\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: no (minimal twist has level 177)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 320 q^{4} + 80 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q - 320 q^{4} + 80 q^{7} + 3944 q^{16} + 528 q^{17} + 444 q^{19} - 444 q^{20} + 1304 q^{22} + 4880 q^{25} + 1452 q^{26} - 1160 q^{28} + 996 q^{29} - 10320 q^{35} + 5196 q^{41} - 10476 q^{46} + 5104 q^{49} + 2184 q^{53} + 11736 q^{59} - 15240 q^{62} - 81012 q^{64} - 29568 q^{68} + 5964 q^{71} - 14376 q^{74} + 3480 q^{76} + 19020 q^{79} - 33096 q^{80} + 20220 q^{85} + 65880 q^{86} - 14932 q^{88} - 17864 q^{94} - 11004 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
235.1 − 7.81880i 0 −45.1337 −21.3172 0 −30.7266 227.790i 0 166.675i
235.2 − 7.77798i 0 −44.4970 −28.5836 0 72.7001 221.650i 0 222.323i
235.3 − 7.65331i 0 −42.5731 38.1687 0 −35.1454 203.372i 0 − 292.117i
235.4 − 6.76718i 0 −29.7948 −6.77685 0 45.8846 93.3518i 0 45.8602i
235.5 − 6.70986i 0 −29.0222 41.0870 0 −6.70931 87.3773i 0 − 275.688i
235.6 − 6.10324i 0 −21.2495 12.8499 0 4.61608 32.0389i 0 − 78.4262i
235.7 − 5.77154i 0 −17.3107 −34.3452 0 −39.2727 7.56484i 0 198.225i
235.8 − 4.96663i 0 −8.66741 −41.3974 0 1.08721 − 36.4182i 0 205.606i
235.9 − 4.85825i 0 −7.60257 12.5087 0 50.4755 − 40.7968i 0 − 60.7705i
235.10 − 4.64719i 0 −5.59638 0.691812 0 −76.1022 − 48.3476i 0 − 3.21498i
235.11 − 4.10319i 0 −0.836195 39.6276 0 −85.8400 − 62.2200i 0 − 162.600i
235.12 − 4.05068i 0 −0.408022 16.4107 0 47.3137 − 63.1581i 0 − 66.4744i
235.13 − 3.44422i 0 4.13738 16.2205 0 92.6602 − 69.3575i 0 − 55.8670i
235.14 − 2.43119i 0 10.0893 −25.9319 0 −17.4595 − 63.4281i 0 63.0454i
235.15 − 2.33963i 0 10.5261 −30.0439 0 −41.7287 − 62.0613i 0 70.2916i
235.16 − 2.31914i 0 10.6216 38.6371 0 9.48964 − 61.7392i 0 − 89.6048i
235.17 − 2.15560i 0 11.3534 −30.9385 0 73.3307 − 58.9629i 0 66.6909i
235.18 − 1.07792i 0 14.8381 −26.1400 0 49.1298 − 33.2410i 0 28.1769i
235.19 − 0.850217i 0 15.2771 11.2738 0 −26.4494 − 26.5923i 0 − 9.58520i
235.20 − 0.389117i 0 15.8486 17.9988 0 −47.2538 − 12.3928i 0 − 7.00365i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 235.40
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 531.5.c.d 40
3.b odd 2 1 177.5.c.a ✓ 40
59.b odd 2 1 inner 531.5.c.d 40
177.d even 2 1 177.5.c.a ✓ 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
177.5.c.a ✓ 40 3.b odd 2 1
177.5.c.a ✓ 40 177.d even 2 1
531.5.c.d 40 1.a even 1 1 trivial
531.5.c.d 40 59.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{40} + 480 T_{2}^{38} + 105254 T_{2}^{36} + 13983422 T_{2}^{34} + 1258795641 T_{2}^{32} + \cdots + 23\!\cdots\!36 \) acting on \(S_{5}^{\mathrm{new}}(531, [\chi])\). Copy content Toggle raw display