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Properties

Label 152.5.k.b
Level $152$
Weight $5$
Character orbit 152.k
Analytic conductor $15.712$
Analytic rank $0$
Dimension $152$
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] = [152,5,Mod(11,152)]
 
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([3, 3, 4]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("152.11");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 152.k (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: \(15.7122343887\)
Analytic rank: \(0\)
Dimension: \(152\)
Relative dimension: \(76\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 152 q + 7 q^{2} + 12 q^{3} + 17 q^{4} + 69 q^{6} - 350 q^{8} - 1872 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 152 q + 7 q^{2} + 12 q^{3} + 17 q^{4} + 69 q^{6} - 350 q^{8} - 1872 q^{9} + 116 q^{10} - 100 q^{11} - 290 q^{12} + 60 q^{14} + 749 q^{16} - 1150 q^{17} - 1324 q^{18} - 274 q^{19} + 384 q^{20} + 1217 q^{22} + 821 q^{24} + 9998 q^{25} + 2868 q^{26} - 4584 q^{27} + 2340 q^{28} + 3832 q^{30} - 83 q^{32} + 3198 q^{33} - 808 q^{34} - 3936 q^{35} - 1032 q^{36} + 772 q^{38} + 6470 q^{40} + 2348 q^{41} - 612 q^{42} - 7006 q^{43} - 4669 q^{44} - 1372 q^{46} + 6583 q^{48} - 51880 q^{49} + 6850 q^{50} - 3682 q^{51} + 1612 q^{52} + 13749 q^{54} + 3456 q^{56} - 1614 q^{57} + 4084 q^{58} + 236 q^{59} + 414 q^{60} + 9642 q^{62} - 9058 q^{64} - 2508 q^{65} + 8491 q^{66} + 2252 q^{67} + 67556 q^{68} + 19896 q^{70} + 6768 q^{72} - 5828 q^{73} + 16542 q^{74} - 79716 q^{75} + 16991 q^{76} - 35198 q^{78} + 1116 q^{80} - 21124 q^{81} + 11583 q^{82} - 1636 q^{83} - 45360 q^{84} - 47140 q^{86} - 29278 q^{88} + 10946 q^{89} + 41846 q^{90} + 4800 q^{91} + 21342 q^{92} + 48304 q^{94} - 39030 q^{96} + 10428 q^{97} + 15751 q^{98} + 23296 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
11.1 −3.99951 − 0.0624750i 8.34918 − 14.4612i 15.9922 + 0.499739i 23.3577 + 13.4856i −34.2961 + 57.3161i − 16.3364i −63.9298 − 2.99782i −98.9176 − 171.330i −92.5770 − 55.3951i
11.2 −3.99924 − 0.0781212i −4.15737 + 7.20078i 15.9878 + 0.624850i 20.9152 + 12.0754i 17.1889 − 28.4729i − 87.7238i −63.8902 − 3.74791i 5.93249 + 10.2754i −82.7014 − 49.9262i
11.3 −3.99568 + 0.185888i 5.48379 − 9.49819i 15.9309 − 1.48550i −38.6512 − 22.3153i −20.1458 + 38.9711i − 60.4791i −63.3786 + 8.89695i −19.6438 − 34.0241i 158.586 + 81.9800i
11.4 −3.98858 − 0.302064i −8.10243 + 14.0338i 15.8175 + 2.40961i −2.54743 − 1.47076i 36.5563 − 53.5275i 65.3782i −62.3615 − 14.3888i −90.7987 − 157.268i 9.71635 + 6.63572i
11.5 −3.94034 − 0.688289i −4.19469 + 7.26541i 15.0525 + 5.42418i −25.4573 − 14.6978i 21.5292 − 25.7410i − 32.6777i −55.5786 − 31.7336i 5.30918 + 9.19576i 90.1941 + 75.4363i
11.6 −3.89589 − 0.906661i 0.229138 − 0.396879i 14.3559 + 7.06451i 10.6026 + 6.12142i −1.25253 + 1.33845i 65.4645i −49.5240 − 40.5385i 40.3950 + 69.9662i −35.7566 − 33.4614i
11.7 −3.88677 − 0.945009i 5.06940 − 8.78046i 14.2139 + 7.34606i −21.6307 − 12.4885i −28.0012 + 29.3370i 65.5747i −48.3041 − 41.9847i −10.8977 − 18.8753i 72.2717 + 68.9810i
11.8 −3.87648 + 0.986347i 2.78728 − 4.82770i 14.0542 − 7.64711i 13.1401 + 7.58643i −6.04304 + 21.4637i 14.3002i −46.9383 + 43.5063i 24.9622 + 43.2358i −58.4202 − 16.4480i
11.9 −3.86235 + 1.04032i −4.16542 + 7.21473i 13.8355 − 8.03613i 27.3002 + 15.7618i 8.58272 − 32.1991i 38.7813i −45.0773 + 45.4316i 5.79849 + 10.0433i −121.840 − 32.4767i
11.10 −3.72627 + 1.45428i 1.29163 − 2.23717i 11.7702 − 10.8380i −7.66990 − 4.42822i −1.55951 + 10.2147i − 17.5818i −28.0973 + 57.5025i 37.1634 + 64.3688i 35.0200 + 5.34659i
11.11 −3.66152 − 1.61037i 2.85363 − 4.94264i 10.8134 + 11.7928i 26.4997 + 15.2996i −18.4081 + 13.5021i − 45.9028i −20.6026 − 60.5932i 24.2136 + 41.9391i −72.3911 − 98.6942i
11.12 −3.58880 + 1.76650i −6.49753 + 11.2540i 9.75899 − 12.6792i −30.1988 − 17.4353i 3.43811 − 51.8664i − 16.2704i −12.6253 + 62.7423i −43.9357 − 76.0989i 139.177 + 9.22573i
11.13 −3.40668 − 2.09632i −2.25903 + 3.91276i 7.21091 + 14.2830i −21.5350 − 12.4333i 15.8982 − 8.59387i 6.08116i 5.37638 − 63.7738i 30.2935 + 52.4699i 47.2989 + 87.5004i
11.14 −3.32568 + 2.22257i −2.13535 + 3.69854i 6.12035 − 14.7831i −31.4054 − 18.1319i −1.11876 − 17.0461i 83.4066i 12.5022 + 62.7670i 31.3805 + 54.3527i 144.744 − 9.49972i
11.15 −3.14415 + 2.47271i 7.48488 − 12.9642i 3.77139 − 15.5492i −14.3348 − 8.27618i 8.52311 + 59.2694i 82.8297i 26.5908 + 58.2145i −71.5470 − 123.923i 65.5353 − 9.42417i
11.16 −3.13004 + 2.49056i −6.05508 + 10.4877i 3.59425 − 15.5911i 25.9992 + 15.0106i −7.16762 − 47.9074i − 11.5045i 27.5803 + 57.7523i −32.8280 − 56.8598i −118.763 + 17.7686i
11.17 −3.07783 − 2.55479i −7.83359 + 13.5682i 2.94612 + 15.7264i 16.9119 + 9.76408i 58.7743 − 21.7474i − 33.7577i 31.1100 − 55.9300i −82.2302 − 142.427i −27.1068 − 73.2585i
11.18 −3.04432 − 2.59464i −1.84174 + 3.18998i 2.53571 + 15.7978i 35.9171 + 20.7367i 13.8837 − 4.93267i 66.7996i 33.2701 − 54.6727i 33.7160 + 58.3979i −55.5386 − 156.321i
11.19 −3.02824 + 2.61338i 6.56385 − 11.3689i 2.34046 − 15.8279i −3.09085 − 1.78450i 9.83443 + 51.5816i − 53.4263i 34.2769 + 54.0472i −45.6682 − 79.0996i 14.0234 − 2.67367i
11.20 −3.01446 − 2.62927i 6.69856 − 11.6023i 2.17392 + 15.8516i −10.4857 − 6.05392i −50.6979 + 17.3622i 19.7415i 35.1250 − 53.4999i −49.2415 − 85.2887i 15.6913 + 45.8190i
See next 80 embeddings (of 152 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 11.76
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.d odd 2 1 inner
19.c even 3 1 inner
152.k odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 152.5.k.b ✓ 152
8.d odd 2 1 inner 152.5.k.b ✓ 152
19.c even 3 1 inner 152.5.k.b ✓ 152
152.k odd 6 1 inner 152.5.k.b ✓ 152
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
152.5.k.b ✓ 152 1.a even 1 1 trivial
152.5.k.b ✓ 152 8.d odd 2 1 inner
152.5.k.b ✓ 152 19.c even 3 1 inner
152.5.k.b ✓ 152 152.k odd 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{76} - 6 T_{3}^{75} + 2025 T_{3}^{74} - 10666 T_{3}^{73} + 2225894 T_{3}^{72} + \cdots + 13\!\cdots\!81 \) acting on \(S_{5}^{\mathrm{new}}(152, [\chi])\). Copy content Toggle raw display