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Properties

Label 825.2.bd.a
Level $825$
Weight $2$
Character orbit 825.bd
Analytic conductor $6.588$
Analytic rank $0$
Dimension $464$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(281,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 4, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.281");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.bd (of order \(10\), degree \(4\), 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: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(464\)
Relative dimension: \(116\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 464 q - 8 q^{3} - 114 q^{4} + 5 q^{6} - 30 q^{7} - 4 q^{9} + 10 q^{10} - 14 q^{12} - 2 q^{15} - 86 q^{16} - 10 q^{18} - 15 q^{21} - 22 q^{22} - 40 q^{24} + 18 q^{25} - 14 q^{27} - 40 q^{28} - 20 q^{30}+ \cdots + 23 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
281.1 −2.20416 + 1.60142i 1.25438 − 1.19437i 1.67575 − 5.15744i −2.13665 + 0.659325i −0.852173 + 4.64137i −1.51240 − 2.08164i 2.88175 + 8.86911i 0.146950 − 2.99640i 3.65367 − 4.87493i
281.2 −2.18337 + 1.58631i 1.72299 + 0.176909i 1.63268 − 5.02489i 1.09099 − 1.95186i −4.04256 + 2.34694i −0.304112 − 0.418574i 2.73833 + 8.42771i 2.93741 + 0.609626i 0.714222 + 5.99227i
281.3 −2.16412 + 1.57232i −1.53523 + 0.801919i 1.59317 − 4.90327i 2.14753 + 0.622979i 2.06154 − 4.14932i −2.26400 − 3.11612i 2.60848 + 8.02807i 1.71385 − 2.46226i −5.62703 + 2.02842i
281.4 −2.16050 + 1.56970i −1.38393 − 1.04150i 1.58578 − 4.88054i 0.110245 − 2.23335i 4.62483 + 0.0778170i 1.98404 + 2.73080i 2.58440 + 7.95397i 0.830539 + 2.88274i 3.26749 + 4.99820i
281.5 −2.14689 + 1.55981i −1.12584 + 1.31624i 1.55810 − 4.79535i −2.18598 + 0.470628i 0.363983 − 4.58191i 1.49728 + 2.06083i 2.49467 + 7.67779i −0.464960 − 2.96375i 3.95897 − 4.42009i
281.6 −2.11420 + 1.53605i 0.411482 + 1.68246i 1.49233 − 4.59293i 0.753422 + 2.10532i −3.45431 − 2.92500i 1.71202 + 2.35639i 2.28480 + 7.03189i −2.66137 + 1.38461i −4.82676 − 3.29376i
281.7 −2.07007 + 1.50399i −1.68242 − 0.411654i 1.40516 − 4.32463i −0.534610 + 2.17122i 4.10185 − 1.67820i −0.0704560 − 0.0969743i 2.01405 + 6.19860i 2.66108 + 1.38515i −2.15882 − 5.29862i
281.8 −2.04004 + 1.48217i −0.551464 − 1.64192i 1.34688 − 4.14526i 1.84572 − 1.26227i 3.55861 + 2.53220i −2.55571 − 3.51763i 1.83786 + 5.65636i −2.39177 + 1.81092i −1.89442 + 5.31075i
281.9 −1.99834 + 1.45188i −0.136528 + 1.72666i 1.26738 − 3.90059i −1.54760 − 1.61398i −2.23408 − 3.64868i −2.57895 − 3.54962i 1.60394 + 4.93642i −2.96272 − 0.471475i 5.43594 + 0.978351i
281.10 −1.94958 + 1.41646i 1.70448 + 0.307837i 1.17650 − 3.62089i 1.84858 + 1.25808i −3.75906 + 1.81416i −1.10506 − 1.52099i 1.34580 + 4.14194i 2.81047 + 1.04940i −5.38597 + 0.165695i
281.11 −1.94870 + 1.41581i 1.08801 + 1.34768i 1.17486 − 3.61586i −1.10432 − 1.94434i −4.02826 − 1.08581i 0.699142 + 0.962287i 1.34125 + 4.12795i −0.632482 + 2.93257i 4.90482 + 2.22542i
281.12 −1.89846 + 1.37931i 0.827595 − 1.52154i 1.08362 − 3.33504i −1.41111 − 1.73458i 0.527524 + 4.03010i 1.48322 + 2.04148i 1.09256 + 3.36255i −1.63017 − 2.51844i 5.07147 + 1.34666i
281.13 −1.89211 + 1.37470i −0.973640 − 1.43249i 1.07224 − 3.30003i −2.20999 − 0.340492i 3.81147 + 1.37196i −0.941561 − 1.29595i 1.06229 + 3.26940i −1.10405 + 2.78946i 4.64961 − 2.39382i
281.14 −1.87941 + 1.36547i 0.325550 + 1.70118i 1.04963 − 3.23043i 2.21204 − 0.326921i −2.93475 − 2.75268i 0.0106902 + 0.0147139i 1.00263 + 3.08577i −2.78803 + 1.10764i −3.71092 + 3.63489i
281.15 −1.81186 + 1.31639i 1.70337 − 0.313899i 0.931910 − 2.86812i −0.213344 + 2.22587i −2.67305 + 2.81104i 1.99220 + 2.74203i 0.702951 + 2.16346i 2.80293 − 1.06937i −2.54357 − 4.31380i
281.16 −1.74548 + 1.26817i −1.71691 − 0.228503i 0.820423 − 2.52500i 2.23486 + 0.0734295i 3.28662 − 1.77848i 2.35078 + 3.23557i 0.436662 + 1.34391i 2.89557 + 0.784639i −3.99403 + 2.70601i
281.17 −1.68896 + 1.22710i −0.196078 − 1.72092i 0.728782 − 2.24296i 2.23224 + 0.130831i 2.44291 + 2.66596i 1.10379 + 1.51924i 0.231206 + 0.711580i −2.92311 + 0.674866i −3.93071 + 2.51822i
281.18 −1.63379 + 1.18702i −1.49672 + 0.871674i 0.642227 − 1.97657i −0.0158726 − 2.23601i 1.41064 − 3.20077i −0.480412 − 0.661230i 0.0488574 + 0.150368i 1.48037 − 2.60931i 2.68012 + 3.63434i
281.19 −1.62747 + 1.18243i 0.0504497 − 1.73132i 0.632497 − 1.94663i −0.951707 + 2.02343i 1.96505 + 2.87732i 1.14275 + 1.57286i 0.0290944 + 0.0895434i −2.99491 − 0.174689i −0.843678 − 4.41840i
281.20 −1.61806 + 1.17559i 0.892373 + 1.48448i 0.618080 − 1.90226i −1.07525 + 1.96057i −3.18906 − 1.35291i −1.33043 − 1.83118i 9.23955e−5 0 0.000284364i −1.40734 + 2.64941i −0.565006 − 4.43639i
See next 80 embeddings (of 464 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 281.116
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
275.bc odd 10 1 inner
825.bd even 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 825.2.bd.a ✓ 464
3.b odd 2 1 inner 825.2.bd.a ✓ 464
11.d odd 10 1 825.2.cg.a yes 464
25.d even 5 1 825.2.cg.a yes 464
33.f even 10 1 825.2.cg.a yes 464
75.j odd 10 1 825.2.cg.a yes 464
275.bc odd 10 1 inner 825.2.bd.a ✓ 464
825.bd even 10 1 inner 825.2.bd.a ✓ 464
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
825.2.bd.a ✓ 464 1.a even 1 1 trivial
825.2.bd.a ✓ 464 3.b odd 2 1 inner
825.2.bd.a ✓ 464 275.bc odd 10 1 inner
825.2.bd.a ✓ 464 825.bd even 10 1 inner
825.2.cg.a yes 464 11.d odd 10 1
825.2.cg.a yes 464 25.d even 5 1
825.2.cg.a yes 464 33.f even 10 1
825.2.cg.a yes 464 75.j odd 10 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(825, [\chi])\).