Properties

Label 154.2.n.a
Level $154$
Weight $2$
Character orbit 154.n
Analytic conductor $1.230$
Analytic rank $0$
Dimension $64$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [154,2,Mod(17,154)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(154, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([5, 27]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("154.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.n (of order \(30\), degree \(8\), 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: \(1.22969619113\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(8\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 8 q^{4} + 12 q^{5} - 10 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 64 q - 8 q^{4} + 12 q^{5} - 10 q^{7} + 4 q^{9} - 8 q^{11} - 2 q^{14} - 12 q^{15} + 8 q^{16} - 30 q^{17} + 8 q^{22} - 16 q^{23} - 20 q^{25} - 24 q^{26} + 10 q^{28} + 20 q^{29} - 18 q^{31} - 126 q^{33} + 30 q^{35} - 32 q^{36} + 16 q^{37} - 12 q^{38} + 20 q^{39} - 30 q^{40} - 2 q^{42} - 2 q^{44} + 108 q^{45} - 24 q^{47} - 78 q^{49} - 60 q^{51} + 8 q^{53} + 4 q^{56} - 80 q^{57} - 28 q^{58} - 60 q^{59} + 4 q^{60} + 30 q^{61} + 50 q^{63} + 16 q^{64} + 72 q^{66} - 32 q^{67} + 30 q^{68} - 10 q^{70} - 8 q^{71} + 20 q^{72} + 90 q^{73} + 20 q^{74} + 180 q^{75} + 46 q^{77} + 96 q^{78} + 30 q^{79} + 18 q^{80} + 48 q^{81} + 60 q^{82} + 40 q^{84} + 140 q^{85} + 10 q^{86} + 14 q^{88} - 36 q^{89} + 106 q^{91} + 28 q^{92} + 94 q^{93} - 120 q^{94} - 70 q^{95} + 104 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 −0.743145 0.669131i −1.26932 2.85094i 0.104528 + 0.994522i −0.660681 3.10826i −0.964361 + 2.96800i 2.06657 + 1.65206i 0.587785 0.809017i −4.50928 + 5.00806i −1.58885 + 2.75197i
17.2 −0.743145 0.669131i −0.288057 0.646987i 0.104528 + 0.994522i 0.507623 + 2.38818i −0.218851 + 0.673553i 2.40050 + 1.11248i 0.587785 0.809017i 1.67178 1.85670i 1.22077 2.11443i
17.3 −0.743145 0.669131i 0.242993 + 0.545771i 0.104528 + 0.994522i −0.828137 3.89608i 0.184613 0.568181i −2.64015 + 0.172111i 0.587785 0.809017i 1.76857 1.96420i −1.99156 + 3.44948i
17.4 −0.743145 0.669131i 1.31438 + 2.95215i 0.104528 + 0.994522i −0.0248203 0.116770i 0.998599 3.07337i 1.24260 2.33580i 0.587785 0.809017i −4.98021 + 5.53108i −0.0596895 + 0.103385i
17.5 0.743145 + 0.669131i −0.795049 1.78571i 0.104528 + 0.994522i −0.578901 2.72352i 0.604036 1.85903i −0.540264 2.59000i −0.587785 + 0.809017i −0.549265 + 0.610021i 1.39218 2.41133i
17.6 0.743145 + 0.669131i −0.655191 1.47158i 0.104528 + 0.994522i 0.737883 + 3.47147i 0.497779 1.53201i 2.53479 0.758189i −0.587785 + 0.809017i 0.271110 0.301098i −1.77451 + 3.07354i
17.7 0.743145 + 0.669131i 0.491544 + 1.10403i 0.104528 + 0.994522i −0.307168 1.44511i −0.373449 + 1.14936i 1.23185 + 2.34148i −0.587785 + 0.809017i 1.03013 1.14408i 0.738698 1.27946i
17.8 0.743145 + 0.669131i 0.958696 + 2.15327i 0.104528 + 0.994522i −0.0111506 0.0524597i −0.728367 + 2.24168i −1.55622 2.13967i −0.587785 + 0.809017i −1.71007 + 1.89922i 0.0268158 0.0464464i
19.1 −0.994522 + 0.104528i −1.54204 1.38846i 0.978148 0.207912i 1.40155 + 3.14793i 1.67872 + 1.21966i 0.662121 2.56156i −0.951057 + 0.309017i 0.136481 + 1.29853i −1.72292 2.98419i
19.2 −0.994522 + 0.104528i −1.17132 1.05466i 0.978148 0.207912i −0.450544 1.01194i 1.27514 + 0.926445i −2.33469 + 1.24468i −0.951057 + 0.309017i −0.0539063 0.512885i 0.553852 + 0.959299i
19.3 −0.994522 + 0.104528i 0.679730 + 0.612031i 0.978148 0.207912i 0.418703 + 0.940423i −0.739981 0.537628i 0.184148 + 2.63934i −0.951057 + 0.309017i −0.226135 2.15153i −0.514710 0.891504i
19.4 −0.994522 + 0.104528i 2.03362 + 1.83108i 0.978148 0.207912i 0.405705 + 0.911227i −2.21388 1.60848i 1.62068 2.09127i −0.951057 + 0.309017i 0.469175 + 4.46390i −0.498731 0.863828i
19.5 0.994522 0.104528i −1.40184 1.26222i 0.978148 0.207912i −1.61021 3.61659i −1.52610 1.10878i −1.72212 + 2.00856i 0.951057 0.309017i 0.0583646 + 0.555302i −1.97943 3.42847i
19.6 0.994522 0.104528i −0.572295 0.515297i 0.978148 0.207912i 0.136527 + 0.306644i −0.623023 0.452653i 2.46505 0.960996i 0.951057 0.309017i −0.251594 2.39376i 0.167832 + 0.290693i
19.7 0.994522 0.104528i 0.118353 + 0.106566i 0.978148 0.207912i 1.34550 + 3.02205i 0.128844 + 0.0936108i −2.10827 + 1.59850i 0.951057 0.309017i −0.310934 2.95834i 1.65402 + 2.86485i
19.8 0.994522 0.104528i 1.85578 + 1.67095i 0.978148 0.207912i −0.776435 1.74390i 2.02028 + 1.46782i −2.08284 1.63149i 0.951057 0.309017i 0.338255 + 3.21829i −0.954469 1.65319i
61.1 −0.207912 + 0.978148i −3.10364 0.326206i −0.913545 0.406737i 2.36149 2.12630i 0.964361 2.96800i 0.932594 + 2.47594i 0.587785 0.809017i 6.59174 + 1.40112i 1.58885 + 2.75197i
61.2 −0.207912 + 0.978148i −0.704336 0.0740287i −0.913545 0.406737i −1.81441 + 1.63370i 0.218851 0.673553i 0.316242 + 2.62678i 0.587785 0.809017i −2.44383 0.519453i −1.22077 2.11443i
61.3 −0.207912 + 0.978148i 0.594148 + 0.0624475i −0.913545 0.406737i 2.96003 2.66523i −0.184613 + 0.568181i 0.979538 2.45774i 0.587785 0.809017i −2.58533 0.549529i 1.99156 + 3.44948i
61.4 −0.207912 + 0.978148i 3.21383 + 0.337787i −0.913545 0.406737i 0.0887159 0.0798801i −0.998599 + 3.07337i −2.60546 + 0.459985i 0.587785 0.809017i 7.28016 + 1.54745i 0.0596895 + 0.103385i
See all 64 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 17.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.d odd 6 1 inner
11.d odd 10 1 inner
77.n even 30 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 154.2.n.a 64
7.d odd 6 1 inner 154.2.n.a 64
11.d odd 10 1 inner 154.2.n.a 64
77.n even 30 1 inner 154.2.n.a 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.2.n.a 64 1.a even 1 1 trivial
154.2.n.a 64 7.d odd 6 1 inner
154.2.n.a 64 11.d odd 10 1 inner
154.2.n.a 64 77.n even 30 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(154, [\chi])\).