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Properties

Label 152.4.p.a
Level $152$
Weight $4$
Character orbit 152.p
Analytic conductor $8.968$
Analytic rank $0$
Dimension $116$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [152,4,Mod(45,152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(152, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("152.45");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 152.p (of order \(6\), degree \(2\), 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: \(8.96829032087\)
Analytic rank: \(0\)
Dimension: \(116\)
Relative dimension: \(58\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 116 q - q^{2} - 7 q^{4} - 11 q^{6} - 8 q^{7} - 46 q^{8} + 484 q^{9} - 44 q^{10} - 58 q^{12} + 24 q^{14} - 230 q^{15} - 67 q^{16} - 2 q^{17} + 196 q^{18} - 840 q^{20} + 137 q^{22} - 2 q^{23} + 77 q^{24}+ \cdots + 55 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
45.1 −2.82711 − 0.0864225i 4.26220 − 2.46078i 7.98506 + 0.488651i −8.57414 + 4.95028i −12.2624 + 6.58855i 24.1590 −22.5324 − 2.07156i −1.38908 + 2.40596i 24.6678 − 13.2540i
45.2 −2.82486 + 0.142059i −7.04526 + 4.06758i 7.95964 − 0.802590i −4.40862 + 2.54532i 19.3240 − 12.4912i 19.7207 −22.3708 + 3.39794i 19.5905 − 33.9317i 12.0922 − 7.81645i
45.3 −2.82331 − 0.170085i −5.08710 + 2.93704i 7.94214 + 0.960407i 17.9631 − 10.3710i 14.8620 − 7.42692i −14.4987 −22.2598 − 4.06237i 3.75238 − 6.49931i −52.4794 + 26.2253i
45.4 −2.81727 + 0.250933i 8.39713 − 4.84809i 7.87406 − 1.41390i −7.24805 + 4.18466i −22.4405 + 15.7655i −14.4081 −21.8286 + 5.95920i 33.5079 − 58.0374i 19.3697 − 13.6081i
45.5 −2.74034 − 0.700393i 1.33173 − 0.768876i 7.01890 + 3.83863i −0.690311 + 0.398551i −4.18791 + 1.17424i −7.42713 −16.5456 − 15.4351i −12.3177 + 21.3348i 2.17083 − 0.608676i
45.6 −2.73439 − 0.723246i −5.03629 + 2.90770i 6.95383 + 3.95528i −17.1051 + 9.87563i 15.8742 − 4.30833i −30.7136 −16.1539 − 15.8446i 3.40947 − 5.90537i 53.9146 − 14.6327i
45.7 −2.66177 + 0.956557i 3.22382 − 1.86127i 6.17000 − 5.09226i 15.4187 − 8.90199i −6.80063 + 8.03803i 36.5436 −11.5520 + 19.4564i −6.57134 + 11.3819i −32.5257 + 38.4439i
45.8 −2.61512 + 1.07757i 2.09100 − 1.20724i 5.67769 − 5.63594i 3.32294 − 1.91850i −4.16734 + 5.41028i −25.0171 −8.77472 + 20.8568i −10.5851 + 18.3340i −6.62257 + 8.59781i
45.9 −2.55889 + 1.20502i −4.74696 + 2.74066i 5.09583 − 6.16705i 2.75286 − 1.58936i 8.84438 − 12.7332i 6.39182 −5.60823 + 21.9214i 1.52239 − 2.63686i −5.12904 + 7.38426i
45.10 −2.41786 − 1.46764i 6.82189 − 3.93862i 3.69206 + 7.09709i 12.0425 − 6.95276i −22.2748 − 0.489060i 3.48301 1.48909 − 22.5784i 17.5255 − 30.3550i −39.3213 − 0.863327i
45.11 −2.38043 − 1.52759i −1.64191 + 0.947957i 3.33293 + 7.27266i 7.43335 − 4.29165i 5.35655 + 0.251620i 3.63601 3.17585 − 22.4034i −11.7028 + 20.2698i −24.2505 − 1.13915i
45.12 −2.37410 + 1.53742i −0.934984 + 0.539813i 3.27269 − 7.29997i −16.9708 + 9.79810i 1.38982 − 2.71903i 1.96699 3.45341 + 22.3623i −12.9172 + 22.3733i 25.2266 − 49.3529i
45.13 −2.06790 − 1.92971i −7.17990 + 4.14532i 0.552429 + 7.98090i −0.378089 + 0.218290i 22.8466 + 5.28303i 17.0792 14.2585 − 17.5697i 20.8673 − 36.1433i 1.20309 + 0.278201i
45.14 −1.96964 + 2.02991i 7.73504 − 4.46582i −0.241064 − 7.99637i 8.20718 − 4.73842i −6.16999 + 24.4975i −1.12317 16.7067 + 15.2606i 26.3872 − 45.7039i −6.54660 + 25.9928i
45.15 −1.95037 − 2.04843i −0.706252 + 0.407755i −0.392134 + 7.99038i −12.8180 + 7.40046i 2.21271 + 0.651437i 26.8247 17.1326 − 14.7809i −13.1675 + 22.8067i 40.1591 + 11.8231i
45.16 −1.90949 − 2.08659i 6.11810 − 3.53229i −0.707710 + 7.96864i −15.3833 + 8.88152i −19.0529 − 6.02110i −5.95523 17.9786 − 13.7393i 11.4541 − 19.8390i 47.9062 + 15.1394i
45.17 −1.85453 + 2.13558i −8.17248 + 4.71838i −1.12144 − 7.92101i 0.978198 − 0.564763i 5.07960 − 26.2034i −30.0678 18.9957 + 12.2948i 31.0262 − 53.7390i −0.607999 + 3.13639i
45.18 −1.57710 + 2.34792i 5.02331 − 2.90021i −3.02550 − 7.40583i −10.8661 + 6.27356i −1.11280 + 16.3683i 0.00550543 22.1599 + 4.57612i 3.32241 − 5.75457i 2.40715 − 35.4069i
45.19 −1.53199 + 2.37761i −3.41182 + 1.96982i −3.30604 − 7.28492i 2.11879 − 1.22328i 0.543410 − 11.1297i 20.3570 22.3855 + 3.29993i −5.73966 + 9.94138i −0.337465 + 6.91169i
45.20 −1.45458 − 2.42574i 3.96852 − 2.29123i −3.76842 + 7.05684i 3.72792 − 2.15232i −11.3304 − 6.29383i −30.2215 22.5995 − 1.12350i −3.00057 + 5.19714i −10.6435 − 5.91226i
See next 80 embeddings (of 116 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 45.58
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.b even 2 1 inner
19.c even 3 1 inner
152.p even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 152.4.p.a ✓ 116
8.b even 2 1 inner 152.4.p.a ✓ 116
19.c even 3 1 inner 152.4.p.a ✓ 116
152.p even 6 1 inner 152.4.p.a ✓ 116
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
152.4.p.a ✓ 116 1.a even 1 1 trivial
152.4.p.a ✓ 116 8.b even 2 1 inner
152.4.p.a ✓ 116 19.c even 3 1 inner
152.4.p.a ✓ 116 152.p even 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(152, [\chi])\).