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Properties

Label 1805.2.b.m
Level $1805$
Weight $2$
Character orbit 1805.b
Analytic conductor $14.413$
Analytic rank $0$
Dimension $40$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1805,2,Mod(1084,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1805.1084");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.b (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: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9} + 20 q^{11} + 40 q^{16} - 18 q^{20} - 92 q^{24} - 26 q^{25} + 76 q^{26} + 40 q^{30} + 4 q^{35} + 156 q^{36} - 80 q^{39} - 48 q^{44} - 22 q^{45} - 72 q^{49}+ \cdots - 128 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1084.1 − 2.66900i 1.76244i −5.12357 −0.705325 − 2.12191i 4.70394 − 2.20993i 8.33681i −0.106178 −5.66339 + 1.88251i
1084.2 − 2.66900i 1.76244i −5.12357 −0.705325 + 2.12191i 4.70394 2.20993i 8.33681i −0.106178 5.66339 + 1.88251i
1084.3 − 2.55697i 3.05876i −4.53809 1.22552 − 1.87032i 7.82114 1.35232i 6.48981i −6.35598 −4.78235 − 3.13361i
1084.4 − 2.55697i 3.05876i −4.53809 1.22552 + 1.87032i 7.82114 − 1.35232i 6.48981i −6.35598 4.78235 − 3.13361i
1084.5 − 2.42726i − 1.05699i −3.89157 0.123305 − 2.23267i −2.56557 4.52506i 4.59133i 1.88278 −5.41925 − 0.299292i
1084.6 − 2.42726i − 1.05699i −3.89157 0.123305 + 2.23267i −2.56557 − 4.52506i 4.59133i 1.88278 5.41925 − 0.299292i
1084.7 − 1.96724i − 3.10308i −1.87002 −2.04586 − 0.902473i −6.10450 2.84392i − 0.255698i −6.62912 −1.77538 + 4.02469i
1084.8 − 1.96724i − 3.10308i −1.87002 −2.04586 + 0.902473i −6.10450 − 2.84392i − 0.255698i −6.62912 1.77538 + 4.02469i
1084.9 − 1.74138i − 0.766290i −1.03240 2.19703 − 0.415991i −1.33440 2.32579i − 1.68496i 2.41280 −0.724398 − 3.82586i
1084.10 − 1.74138i − 0.766290i −1.03240 2.19703 + 0.415991i −1.33440 − 2.32579i − 1.68496i 2.41280 0.724398 − 3.82586i
1084.11 − 1.47577i − 2.52656i −0.177886 2.11161 − 0.735611i −3.72861 4.13170i − 2.68901i −3.38349 −1.08559 − 3.11624i
1084.12 − 1.47577i − 2.52656i −0.177886 2.11161 + 0.735611i −3.72861 − 4.13170i − 2.68901i −3.38349 1.08559 − 3.11624i
1084.13 − 1.40041i 2.85260i 0.0388655 0.846513 − 2.06964i 3.99479 − 4.34514i − 2.85524i −5.13731 −2.89834 − 1.18546i
1084.14 − 1.40041i 2.85260i 0.0388655 0.846513 + 2.06964i 3.99479 4.34514i − 2.85524i −5.13731 2.89834 − 1.18546i
1084.15 − 0.937092i 1.03012i 1.12186 −1.84457 − 1.26394i 0.965321 − 1.65832i − 2.92547i 1.93884 −1.18443 + 1.72854i
1084.16 − 0.937092i 1.03012i 1.12186 −1.84457 + 1.26394i 0.965321 1.65832i − 2.92547i 1.93884 1.18443 + 1.72854i
1084.17 − 0.717155i 1.56975i 1.48569 0.811198 − 2.08374i 1.12576 − 2.51917i − 2.49978i 0.535883 −1.49436 − 0.581755i
1084.18 − 0.717155i 1.56975i 1.48569 0.811198 + 2.08374i 1.12576 2.51917i − 2.49978i 0.535883 1.49436 − 0.581755i
1084.19 − 0.113485i 1.07621i 1.98712 −1.21941 − 1.87431i 0.122133 1.50555i − 0.452479i 1.84178 −0.212706 + 0.138385i
1084.20 − 0.113485i 1.07621i 1.98712 −1.21941 + 1.87431i 0.122133 − 1.50555i − 0.452479i 1.84178 0.212706 + 0.138385i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1084.40
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
19.b odd 2 1 inner
95.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1805.2.b.m ✓ 40
5.b even 2 1 inner 1805.2.b.m ✓ 40
5.c odd 4 2 9025.2.a.cv 40
19.b odd 2 1 inner 1805.2.b.m ✓ 40
95.d odd 2 1 inner 1805.2.b.m ✓ 40
95.g even 4 2 9025.2.a.cv 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1805.2.b.m ✓ 40 1.a even 1 1 trivial
1805.2.b.m ✓ 40 5.b even 2 1 inner
1805.2.b.m ✓ 40 19.b odd 2 1 inner
1805.2.b.m ✓ 40 95.d odd 2 1 inner
9025.2.a.cv 40 5.c odd 4 2
9025.2.a.cv 40 95.g even 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1805, [\chi])\):

\( T_{2}^{20} + 32 T_{2}^{18} + 431 T_{2}^{16} + 3186 T_{2}^{14} + 14144 T_{2}^{12} + 38798 T_{2}^{10} + \cdots + 80 \) Copy content Toggle raw display
\( T_{29}^{20} - 300 T_{29}^{18} + 37770 T_{29}^{16} - 2590500 T_{29}^{14} + 105058275 T_{29}^{12} + \cdots + 299880050000 \) Copy content Toggle raw display