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Properties

Label 152.2.t.a
Level $152$
Weight $2$
Character orbit 152.t
Analytic conductor $1.214$
Analytic rank $0$
Dimension $108$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [152,2,Mod(5,152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(152, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("152.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.t (of order \(18\), degree \(6\), 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: \(1.21372611072\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(18\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 9 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 12 q^{17} - 12 q^{18} - 42 q^{20} - 12 q^{22} - 12 q^{23} - 36 q^{24} - 12 q^{25} + 21 q^{26} + 24 q^{28} - 48 q^{30} + 30 q^{31} + 39 q^{32} - 30 q^{33} - 60 q^{34} + 69 q^{36} - 42 q^{38} - 24 q^{39} + 36 q^{40} - 24 q^{41} - 81 q^{42} + 45 q^{44} - 18 q^{46} - 48 q^{47} - 21 q^{48} - 24 q^{49} - 12 q^{50} + 3 q^{52} + 63 q^{54} - 42 q^{55} + 30 q^{56} - 12 q^{57} - 84 q^{58} + 30 q^{60} - 6 q^{62} + 30 q^{63} + 3 q^{64} - 6 q^{65} + 54 q^{66} + 36 q^{68} + 123 q^{70} - 12 q^{71} + 150 q^{72} + 12 q^{73} + 75 q^{74} + 42 q^{76} + 39 q^{78} - 12 q^{79} + 51 q^{80} - 18 q^{81} + 99 q^{82} + 75 q^{84} - 48 q^{86} - 6 q^{87} - 27 q^{88} - 12 q^{89} + 66 q^{90} - 48 q^{92} + 54 q^{94} - 72 q^{95} + 42 q^{96} - 12 q^{97} + 93 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1 −1.38607 + 0.280709i 0.791695 + 0.139597i 1.84240 − 0.778168i 1.75641 − 2.09321i −1.13653 + 0.0287440i −0.937036 − 1.62299i −2.33527 + 1.59578i −2.21178 − 0.805024i −1.84694 + 3.39439i
5.2 −1.37736 − 0.320753i 2.07211 + 0.365368i 1.79424 + 0.883583i −1.02643 + 1.22325i −2.73684 − 1.16788i 2.07620 + 3.59608i −2.18789 − 1.79252i 1.34105 + 0.488103i 1.80612 − 1.35562i
5.3 −1.33742 − 0.459694i −2.93045 − 0.516717i 1.57736 + 1.22960i −0.797439 + 0.950351i 3.68169 + 2.03817i −0.292443 − 0.506526i −1.54435 − 2.36960i 5.50144 + 2.00236i 1.50338 − 0.904437i
5.4 −1.24223 + 0.675916i −0.791695 − 0.139597i 1.08628 − 1.67929i −1.75641 + 2.09321i 1.07782 − 0.361707i −0.937036 − 1.62299i −0.214349 + 2.82029i −2.21178 − 0.805024i 0.767037 − 3.78744i
5.5 −0.848942 + 1.13106i −2.07211 − 0.365368i −0.558594 − 1.92041i 1.02643 − 1.22325i 2.17235 − 2.03350i 2.07620 + 3.59608i 2.64631 + 0.998513i 1.34105 + 0.488103i 0.512190 + 2.19942i
5.6 −0.818915 − 1.15299i −1.33117 − 0.234720i −0.658755 + 1.88840i 2.47882 − 2.95414i 0.819482 + 1.72703i −0.0505133 − 0.0874916i 2.71676 − 0.786901i −1.10217 − 0.401157i −5.43603 − 0.438853i
5.7 −0.750154 − 1.19886i 2.37084 + 0.418044i −0.874538 + 1.79866i 0.424827 − 0.506289i −1.27732 − 3.15591i −1.14188 − 1.97779i 2.81238 − 0.300824i 2.62706 + 0.956171i −0.925656 − 0.129514i
5.8 −0.729035 + 1.21182i 2.93045 + 0.516717i −0.937017 − 1.76692i 0.797439 − 0.950351i −2.76257 + 3.17447i −0.292443 − 0.506526i 2.82431 + 0.152648i 5.50144 + 2.00236i 0.570294 + 1.65919i
5.9 −0.466830 − 1.33494i −0.865720 − 0.152650i −1.56414 + 1.24638i −1.97507 + 2.35380i 0.200366 + 1.22695i 1.81690 + 3.14696i 2.39404 + 1.50619i −2.09291 − 0.761756i 4.06421 + 1.53778i
5.10 0.113800 + 1.40963i 1.33117 + 0.234720i −1.97410 + 0.320831i −2.47882 + 2.95414i −0.179382 + 1.90316i −0.0505133 − 0.0874916i −0.676904 − 2.74623i −1.10217 − 0.401157i −4.44633 − 3.15803i
5.11 0.195962 + 1.40057i −2.37084 − 0.418044i −1.92320 + 0.548917i −0.424827 + 0.506289i 0.120905 − 3.40245i −1.14188 − 1.97779i −1.14567 − 2.58601i 2.62706 + 0.956171i −0.792344 − 0.495787i
5.12 0.375145 − 1.36355i −1.36146 − 0.240062i −1.71853 − 1.02306i −0.0771500 + 0.0919438i −0.838080 + 1.76636i −1.99818 − 3.46096i −2.03969 + 1.95951i −1.02314 − 0.372393i 0.0964275 + 0.139690i
5.13 0.500471 + 1.32270i 0.865720 + 0.152650i −1.49906 + 1.32394i 1.97507 − 2.35380i 0.231358 + 1.22148i 1.81690 + 3.14696i −2.50141 − 1.32020i −2.09291 − 0.761756i 4.10183 + 1.43441i
5.14 0.925229 − 1.06956i 2.75922 + 0.486524i −0.287902 − 1.97917i −2.32112 + 2.76621i 3.07327 − 2.50099i −0.692143 − 1.19883i −2.38321 − 1.52326i 4.55749 + 1.65879i 0.811044 + 5.04195i
5.15 1.10645 − 0.880780i −0.186890 − 0.0329537i 0.448453 − 1.94907i 0.638995 − 0.761525i −0.235809 + 0.128147i 0.719104 + 1.24552i −1.22052 − 2.55154i −2.78524 − 1.01374i 0.0362789 − 1.40540i
5.16 1.16385 + 0.803400i 1.36146 + 0.240062i 0.709096 + 1.87008i 0.0771500 − 0.0919438i 1.39167 + 1.37319i −1.99818 − 3.46096i −0.677138 + 2.74618i −1.02314 − 0.372393i 0.163659 − 0.0450265i
5.17 1.39626 + 0.224602i −2.75922 − 0.486524i 1.89911 + 0.627207i 2.32112 − 2.76621i −3.74332 − 1.29904i −0.692143 − 1.19883i 2.51078 + 1.30229i 4.55749 + 1.65879i 3.86220 − 3.34103i
5.18 1.41374 − 0.0364942i 0.186890 + 0.0329537i 1.99734 − 0.103187i −0.638995 + 0.761525i 0.265417 + 0.0397677i 0.719104 + 1.24552i 2.81995 − 0.218771i −2.78524 − 1.01374i −0.875584 + 1.09992i
61.1 −1.38607 − 0.280709i 0.791695 − 0.139597i 1.84240 + 0.778168i 1.75641 + 2.09321i −1.13653 − 0.0287440i −0.937036 + 1.62299i −2.33527 − 1.59578i −2.21178 + 0.805024i −1.84694 − 3.39439i
61.2 −1.37736 + 0.320753i 2.07211 − 0.365368i 1.79424 − 0.883583i −1.02643 − 1.22325i −2.73684 + 1.16788i 2.07620 − 3.59608i −2.18789 + 1.79252i 1.34105 − 0.488103i 1.80612 + 1.35562i
See next 80 embeddings (of 108 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5.18
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.b even 2 1 inner
19.e even 9 1 inner
152.t even 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 152.2.t.a ✓ 108
4.b odd 2 1 608.2.bf.a 108
8.b even 2 1 inner 152.2.t.a ✓ 108
8.d odd 2 1 608.2.bf.a 108
19.e even 9 1 inner 152.2.t.a ✓ 108
76.l odd 18 1 608.2.bf.a 108
152.t even 18 1 inner 152.2.t.a ✓ 108
152.u odd 18 1 608.2.bf.a 108
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
152.2.t.a ✓ 108 1.a even 1 1 trivial
152.2.t.a ✓ 108 8.b even 2 1 inner
152.2.t.a ✓ 108 19.e even 9 1 inner
152.2.t.a ✓ 108 152.t even 18 1 inner
608.2.bf.a 108 4.b odd 2 1
608.2.bf.a 108 8.d odd 2 1
608.2.bf.a 108 76.l odd 18 1
608.2.bf.a 108 152.u odd 18 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(152, [\chi])\).