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Properties

Label 805.2.c.b
Level $805$
Weight $2$
Character orbit 805.c
Analytic conductor $6.428$
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] = [805,2,Mod(484,805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(805, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("805.484");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.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: \(6.42795736271\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 16 q^{4} - 2 q^{5} - 12 q^{6} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 16 q^{4} - 2 q^{5} - 12 q^{6} - 16 q^{9} - 4 q^{10} - 16 q^{11} + 4 q^{14} - 2 q^{15} - 8 q^{16} + 52 q^{19} + 2 q^{20} + 24 q^{24} - 8 q^{25} - 44 q^{26} + 24 q^{29} + 8 q^{30} - 100 q^{31} + 56 q^{34} - 2 q^{35} - 36 q^{36} + 52 q^{39} + 10 q^{40} - 8 q^{41} + 20 q^{44} - 4 q^{45} + 4 q^{46} - 24 q^{49} + 28 q^{50} - 64 q^{51} + 20 q^{54} + 28 q^{55} - 12 q^{56} + 36 q^{59} + 42 q^{60} + 16 q^{61} - 24 q^{64} + 30 q^{65} - 4 q^{66} + 12 q^{70} - 48 q^{71} - 72 q^{74} - 16 q^{75} - 112 q^{76} + 88 q^{79} + 8 q^{80} - 32 q^{81} - 24 q^{84} - 12 q^{85} - 64 q^{86} + 20 q^{89} + 108 q^{90} - 4 q^{91} - 36 q^{94} + 48 q^{95} - 76 q^{96} + 112 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
484.1 − 2.55311i − 0.556415i −4.51835 −0.768635 + 2.09981i −1.42059 1.00000i 6.42962i 2.69040 5.36104 + 1.96241i
484.2 − 2.43455i − 2.82471i −3.92701 1.28007 − 1.83342i −6.87689 1.00000i 4.69139i −4.97900 −4.46354 − 3.11638i
484.3 − 2.37028i 0.134036i −3.61823 −0.502687 − 2.17883i 0.317703 − 1.00000i 3.83566i 2.98203 −5.16444 + 1.19151i
484.4 − 1.76402i 1.09514i −1.11176 1.35079 + 1.78196i 1.93184 − 1.00000i − 1.56687i 1.80068 3.14340 − 2.38282i
484.5 − 1.69164i − 0.285164i −0.861643 −2.21071 + 0.335799i −0.482394 − 1.00000i − 1.92569i 2.91868 0.568051 + 3.73972i
484.6 − 1.53413i 2.66039i −0.353561 −1.51645 − 1.64328i 4.08139 1.00000i − 2.52585i −4.07768 −2.52101 + 2.32644i
484.7 − 1.31562i 2.16083i 0.269134 2.14936 + 0.616662i 2.84283 1.00000i − 2.98533i −1.66917 0.811296 − 2.82774i
484.8 − 1.23080i − 0.767488i 0.485126 1.54864 + 1.61298i −0.944626 1.00000i − 3.05870i 2.41096 1.98526 − 1.90607i
484.9 − 1.11343i − 2.87976i 0.760266 −1.36689 − 1.76964i −3.20642 − 1.00000i − 3.07337i −5.29300 −1.97037 + 1.52194i
484.10 − 0.792462i − 2.09947i 1.37200 −2.02376 − 0.951002i −1.66375 1.00000i − 2.67218i −1.40777 −0.753633 + 1.60375i
484.11 − 0.649823i − 1.89575i 1.57773 −0.686894 + 2.12795i −1.23191 − 1.00000i − 2.32489i −0.593883 1.38279 + 0.446360i
484.12 − 0.271475i 2.40463i 1.92630 1.74717 − 1.39549i 0.652799 − 1.00000i − 1.06589i −2.78227 −0.378841 − 0.474315i
484.13 0.271475i − 2.40463i 1.92630 1.74717 + 1.39549i 0.652799 1.00000i 1.06589i −2.78227 −0.378841 + 0.474315i
484.14 0.649823i 1.89575i 1.57773 −0.686894 − 2.12795i −1.23191 1.00000i 2.32489i −0.593883 1.38279 − 0.446360i
484.15 0.792462i 2.09947i 1.37200 −2.02376 + 0.951002i −1.66375 − 1.00000i 2.67218i −1.40777 −0.753633 − 1.60375i
484.16 1.11343i 2.87976i 0.760266 −1.36689 + 1.76964i −3.20642 1.00000i 3.07337i −5.29300 −1.97037 − 1.52194i
484.17 1.23080i 0.767488i 0.485126 1.54864 − 1.61298i −0.944626 − 1.00000i 3.05870i 2.41096 1.98526 + 1.90607i
484.18 1.31562i − 2.16083i 0.269134 2.14936 − 0.616662i 2.84283 − 1.00000i 2.98533i −1.66917 0.811296 + 2.82774i
484.19 1.53413i − 2.66039i −0.353561 −1.51645 + 1.64328i 4.08139 − 1.00000i 2.52585i −4.07768 −2.52101 − 2.32644i
484.20 1.69164i 0.285164i −0.861643 −2.21071 − 0.335799i −0.482394 1.00000i 1.92569i 2.91868 0.568051 − 3.73972i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 484.24
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 805.2.c.b ✓ 24
5.b even 2 1 inner 805.2.c.b ✓ 24
5.c odd 4 1 4025.2.a.x 12
5.c odd 4 1 4025.2.a.y 12
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.c.b ✓ 24 1.a even 1 1 trivial
805.2.c.b ✓ 24 5.b even 2 1 inner
4025.2.a.x 12 5.c odd 4 1
4025.2.a.y 12 5.c odd 4 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} + 32 T_{2}^{22} + 442 T_{2}^{20} + 3468 T_{2}^{18} + 17133 T_{2}^{16} + 55854 T_{2}^{14} + \cdots + 289 \) acting on \(S_{2}^{\mathrm{new}}(805, [\chi])\). Copy content Toggle raw display