Properties

Label 925.2.bn.b
Level $925$
Weight $2$
Character orbit 925.bn
Analytic conductor $7.386$
Analytic rank $0$
Dimension $204$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [925,2,Mod(18,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.18"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([27, 17])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 925 = 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 925.bn (of order \(36\), degree \(12\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [204] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.38616218697\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(17\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 185)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 204 q + 12 q^{2} + 6 q^{3} - 24 q^{6} + 12 q^{7} + 24 q^{8} - 36 q^{11} - 36 q^{12} + 12 q^{13} - 24 q^{14} - 24 q^{16} + 30 q^{17} + 90 q^{18} - 24 q^{21} + 24 q^{22} + 6 q^{23} + 36 q^{24} - 12 q^{26}+ \cdots + 192 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
18.1 −2.12845 − 1.78598i −0.224601 + 2.56720i 0.993269 + 5.63311i 0 5.06302 − 5.06302i 1.82259 − 0.849888i 5.16800 − 8.95124i −3.58566 − 0.632249i 0
18.2 −1.77583 − 1.49010i 0.0197082 − 0.225266i 0.585884 + 3.32271i 0 −0.370666 + 0.370666i −1.34678 + 0.628014i 1.59256 − 2.75839i 2.90407 + 0.512065i 0
18.3 −1.65259 − 1.38669i 0.212554 − 2.42950i 0.460860 + 2.61366i 0 −3.72023 + 3.72023i 1.00355 − 0.467963i 0.705423 − 1.22183i −2.90287 − 0.511855i 0
18.4 −1.33241 − 1.11802i −0.0386277 + 0.441516i 0.178038 + 1.00970i 0 0.545093 − 0.545093i 3.44535 − 1.60659i −0.847682 + 1.46823i 2.76098 + 0.486835i 0
18.5 −1.15192 − 0.966579i −0.288680 + 3.29963i 0.0453577 + 0.257236i 0 3.52189 − 3.52189i −0.992081 + 0.462615i −1.30734 + 2.26438i −7.84979 − 1.38413i 0
18.6 −0.905964 − 0.760194i 0.280962 − 3.21141i −0.104421 − 0.592199i 0 −2.69583 + 2.69583i −2.07466 + 0.967428i −1.53824 + 2.66430i −7.27977 − 1.28362i 0
18.7 −0.579594 − 0.486337i −0.137564 + 1.57237i −0.247891 − 1.40586i 0 0.844432 − 0.844432i 2.45442 − 1.14451i −1.29665 + 2.24587i 0.501006 + 0.0883409i 0
18.8 −0.413784 − 0.347206i 0.0815557 − 0.932186i −0.296631 − 1.68228i 0 −0.357407 + 0.357407i −0.477205 + 0.222524i −1.00151 + 1.73467i 2.09210 + 0.368894i 0
18.9 −0.231062 − 0.193884i 0.0348827 − 0.398711i −0.331498 − 1.88002i 0 −0.0853640 + 0.0853640i −3.40384 + 1.58724i −0.589540 + 1.02111i 2.79667 + 0.493128i 0
18.10 0.515411 + 0.432481i 0.209080 − 2.38979i −0.268688 − 1.52380i 0 1.14130 − 1.14130i 2.46995 − 1.15176i 1.19335 − 2.06695i −2.71297 − 0.478369i 0
18.11 0.529429 + 0.444244i −0.228834 + 2.61559i −0.264354 − 1.49922i 0 −1.28311 + 1.28311i 0.733878 − 0.342213i 1.21719 − 2.10823i −3.83450 − 0.676127i 0
18.12 0.895658 + 0.751546i −0.181624 + 2.07597i −0.109915 − 0.623360i 0 −1.72286 + 1.72286i −3.47097 + 1.61854i 1.53924 − 2.66603i −1.32223 − 0.233145i 0
18.13 0.926751 + 0.777636i 0.103885 − 1.18742i −0.0931474 − 0.528265i 0 1.01965 − 1.01965i 0.743725 − 0.346805i 1.53426 − 2.65742i 1.55526 + 0.274234i 0
18.14 1.38534 + 1.16244i −0.191341 + 2.18703i 0.220607 + 1.25112i 0 −2.80736 + 2.80736i 4.44146 − 2.07109i 0.659695 − 1.14263i −1.79208 − 0.315992i 0
18.15 1.39978 + 1.17455i 0.0319999 − 0.365761i 0.232506 + 1.31861i 0 0.474398 − 0.474398i −1.06911 + 0.498533i 0.603963 − 1.04610i 2.82167 + 0.497536i 0
18.16 1.95495 + 1.64040i 0.0617260 − 0.705532i 0.783627 + 4.44417i 0 1.27802 − 1.27802i 1.75899 − 0.820228i −3.20625 + 5.55338i 2.46046 + 0.433845i 0
18.17 1.98709 + 1.66737i −0.135184 + 1.54516i 0.821120 + 4.65681i 0 −2.84498 + 2.84498i −3.63042 + 1.69289i −3.53900 + 6.12973i 0.585164 + 0.103180i 0
143.1 −2.28710 + 0.832436i 0.704150 − 0.328351i 3.00578 − 2.52215i 0 −1.33713 + 1.33713i −1.03029 − 0.721419i −2.34111 + 4.05492i −1.54035 + 1.83572i 0
143.2 −2.25816 + 0.821903i 0.775249 − 0.361505i 2.89168 − 2.42640i 0 −1.45352 + 1.45352i 1.49081 + 1.04388i −2.13251 + 3.69362i −1.45804 + 1.73762i 0
143.3 −1.81354 + 0.660073i −1.89554 + 0.883904i 1.32113 − 1.10856i 0 2.85418 − 2.85418i 1.35725 + 0.950354i 0.265744 − 0.460283i 0.883415 − 1.05281i 0
See next 80 embeddings (of 204 total)
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 18.17
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
185.z even 36 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 925.2.bn.b 204
5.b even 2 1 185.2.z.a ✓ 204
5.c odd 4 1 185.2.bc.a yes 204
5.c odd 4 1 925.2.bq.b 204
37.i odd 36 1 925.2.bq.b 204
185.z even 36 1 inner 925.2.bn.b 204
185.ba odd 36 1 185.2.bc.a yes 204
185.bc even 36 1 185.2.z.a ✓ 204
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
185.2.z.a ✓ 204 5.b even 2 1
185.2.z.a ✓ 204 185.bc even 36 1
185.2.bc.a yes 204 5.c odd 4 1
185.2.bc.a yes 204 185.ba odd 36 1
925.2.bn.b 204 1.a even 1 1 trivial
925.2.bn.b 204 185.z even 36 1 inner
925.2.bq.b 204 5.c odd 4 1
925.2.bq.b 204 37.i odd 36 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{204} - 12 T_{2}^{203} + 72 T_{2}^{202} - 304 T_{2}^{201} + 1062 T_{2}^{200} + \cdots + 11\!\cdots\!81 \) acting on \(S_{2}^{\mathrm{new}}(925, [\chi])\). Copy content Toggle raw display