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Properties

Label 931.2.ca.a
Level $931$
Weight $2$
Character orbit 931.ca
Analytic conductor $7.434$
Analytic rank $0$
Dimension $3276$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [931,2,Mod(4,931)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(931, base_ring=CyclotomicField(126))
 
chi = DirichletCharacter(H, H._module([30, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("931.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.ca (of order \(63\), degree \(36\), 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: \(7.43407242818\)
Analytic rank: \(0\)
Dimension: \(3276\)
Relative dimension: \(91\) over \(\Q(\zeta_{63})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{63}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 3276 q - 39 q^{2} - 39 q^{3} - 39 q^{4} - 39 q^{5} - 30 q^{6} - 12 q^{7} - 15 q^{8} - 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 3276 q - 39 q^{2} - 39 q^{3} - 39 q^{4} - 39 q^{5} - 30 q^{6} - 12 q^{7} - 15 q^{8} - 39 q^{9} - 57 q^{10} + 33 q^{12} - 30 q^{13} - 39 q^{14} - 21 q^{15} - 51 q^{16} - 42 q^{17} - 36 q^{18} - 27 q^{19} - 60 q^{21} - 18 q^{22} - 39 q^{23} - 6 q^{24} - 39 q^{25} - 45 q^{26} - 51 q^{27} - 87 q^{28} - 42 q^{29} + 18 q^{30} + 234 q^{31} + 78 q^{32} - 3 q^{33} - 18 q^{34} - 99 q^{35} - 51 q^{36} - 90 q^{37} + 30 q^{38} - 60 q^{39} - 99 q^{40} - 12 q^{41} - 45 q^{42} - 54 q^{43} + 132 q^{44} + 87 q^{45} + 15 q^{46} - 21 q^{47} - 63 q^{48} - 69 q^{50} - 39 q^{51} - 201 q^{52} - 21 q^{53} - 72 q^{54} - 15 q^{55} - 96 q^{56} - 36 q^{57} - 78 q^{58} - 48 q^{59} - 12 q^{60} + 150 q^{61} + 69 q^{62} + 276 q^{63} + 195 q^{64} - 42 q^{65} + 153 q^{66} - 27 q^{67} + 36 q^{68} - 63 q^{69} - 57 q^{70} + 15 q^{71} + 351 q^{72} + 36 q^{73} - 129 q^{74} - 141 q^{75} - 84 q^{76} - 102 q^{77} - 105 q^{78} + 42 q^{79} - 18 q^{80} - 78 q^{81} - 54 q^{82} - 3 q^{83} - 222 q^{84} - 342 q^{85} - 258 q^{86} - 39 q^{87} + 24 q^{88} - 165 q^{89} + 174 q^{90} + 90 q^{91} - 24 q^{92} + 264 q^{93} - 366 q^{94} - 111 q^{95} + 561 q^{96} - 87 q^{97} - 48 q^{98} - 144 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4.1 −1.58755 − 2.20815i 0.229822 − 0.355835i −1.71864 + 5.11527i 2.25790 − 3.49591i −1.15059 + 0.0574237i −0.861056 + 2.50172i 8.82618 − 2.72252i 1.16006 + 2.57096i −11.3040 + 0.564161i
4.2 −1.58598 − 2.20596i 1.04612 − 1.61971i −1.71397 + 5.10137i −0.330937 + 0.512391i −5.23214 + 0.261125i 1.85659 − 1.88496i 8.77934 − 2.70807i −0.295232 − 0.654302i 1.65518 − 0.0826064i
4.3 −1.57704 − 2.19352i 1.08337 − 1.67739i −1.68753 + 5.02268i −1.25067 + 1.93641i −5.38791 + 0.268899i −0.0147245 + 2.64571i 8.51552 − 2.62669i −0.406077 − 0.899959i 6.21992 − 0.310423i
4.4 −1.56064 − 2.17072i −0.514664 + 0.796855i −1.63945 + 4.87957i −0.348726 + 0.539934i 2.53295 − 0.126414i −2.29761 − 1.31186i 8.04132 − 2.48042i 0.863762 + 1.91429i 1.71628 − 0.0856560i
4.5 −1.50087 − 2.08758i −1.57744 + 2.44236i −1.46842 + 4.37053i −2.22686 + 3.44785i 7.46616 − 0.372621i 1.53677 − 2.15368i 6.41398 − 1.97845i −2.24293 − 4.97085i 10.5399 − 0.526025i
4.6 −1.44998 − 2.01681i −0.706405 + 1.09373i −1.32808 + 3.95282i −1.27952 + 1.98108i 3.23012 − 0.161208i −1.52306 + 2.16339i 5.15058 − 1.58874i 0.536626 + 1.18928i 5.85074 − 0.291999i
4.7 −1.44364 − 2.00798i −0.851884 + 1.31898i −1.31091 + 3.90173i 1.58391 − 2.45237i 3.87829 − 0.193557i −0.209203 − 2.63747i 5.00069 − 1.54251i 0.219873 + 0.487289i −7.21090 + 0.359881i
4.8 −1.43318 − 1.99343i −1.70002 + 2.63215i −1.28280 + 3.81805i 1.01940 − 1.57834i 7.68346 − 0.383466i 0.705724 + 2.54989i 4.75735 − 1.46745i −2.80428 − 6.21492i −4.60730 + 0.229941i
4.9 −1.40530 − 1.95465i −0.206373 + 0.319528i −1.20883 + 3.59790i −1.63441 + 2.53056i 0.914585 − 0.0456450i 2.59527 + 0.514370i 4.13055 − 1.27410i 1.17435 + 2.60263i 7.24321 − 0.361494i
4.10 −1.37248 − 1.90900i −1.57263 + 2.43490i −1.12361 + 3.34426i 0.459258 − 0.711071i 6.80662 − 0.339704i −2.39703 − 1.11994i 3.43289 − 1.05891i −2.22173 − 4.92387i −1.98775 + 0.0992047i
4.11 −1.37160 − 1.90778i 1.03880 − 1.60838i −1.12137 + 3.33758i 1.39268 − 2.15629i −4.49326 + 0.224249i 1.06508 − 2.42190i 3.41489 − 1.05335i −0.273913 − 0.607054i −6.02393 + 0.300642i
4.12 −1.32153 − 1.83814i 0.390705 − 0.604930i −0.995340 + 2.96248i 0.149705 − 0.231789i −1.62828 + 0.0812639i −2.64571 + 0.0140364i 2.43420 − 0.750850i 1.02057 + 2.26182i −0.623902 + 0.0311377i
4.13 −1.28657 − 1.78951i 1.49784 − 2.31911i −0.910117 + 2.70882i −1.47538 + 2.28433i −6.07717 + 0.303299i −1.92413 − 1.81596i 1.80624 − 0.557151i −1.90089 − 4.21281i 5.98603 − 0.298750i
4.14 −1.26133 − 1.75440i 0.0971560 − 0.150427i −0.850005 + 2.52991i −0.332977 + 0.515549i −0.386456 + 0.0192872i 2.63431 − 0.245830i 1.38109 − 0.426011i 1.22067 + 2.70529i 1.32448 − 0.0661019i
4.15 −1.24707 − 1.73458i 1.83092 − 2.83482i −0.816583 + 2.43044i 1.26661 − 1.96109i −7.20049 + 0.359362i 2.31665 + 1.27794i 1.15126 − 0.355116i −3.45006 − 7.64612i −4.98122 + 0.248602i
4.16 −1.18020 − 1.64156i −1.05649 + 1.63577i −0.664877 + 1.97891i −0.978648 + 1.51524i 3.93210 − 0.196243i 0.596699 + 2.57759i 0.169268 − 0.0522124i −0.325704 − 0.721834i 3.64237 − 0.181783i
4.17 −1.15213 − 1.60251i 1.03341 − 1.60003i −0.603675 + 1.79675i 1.52460 − 2.36055i −3.75470 + 0.187389i −2.63802 + 0.202176i −0.197183 + 0.0608228i −0.258307 − 0.572468i −5.53935 + 0.276458i
4.18 −1.15063 − 1.60043i 0.580798 − 0.899251i −0.600448 + 1.78714i 1.39314 − 2.15700i −2.10747 + 0.105179i 1.33064 + 2.28679i −0.216013 + 0.0666312i 0.762535 + 1.68995i −5.05510 + 0.252289i
4.19 −1.14113 − 1.58721i −0.732877 + 1.13472i −0.580092 + 1.72656i 1.70401 − 2.63832i 2.63734 − 0.131624i 1.83977 − 1.90138i −0.333620 + 0.102908i 0.483391 + 1.07130i −6.13205 + 0.306038i
4.20 −1.03920 − 1.44544i 1.41971 − 2.19815i −0.372387 + 1.10835i −2.22202 + 3.44035i −4.65266 + 0.232205i 2.57597 + 0.603655i −1.41324 + 0.435928i −1.58240 − 3.50696i 7.28195 − 0.363427i
See next 80 embeddings (of 3276 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 4.91
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
931.ca even 63 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 931.2.ca.a ✓ 3276
19.e even 9 1 931.2.cb.a yes 3276
49.g even 21 1 931.2.cb.a yes 3276
931.ca even 63 1 inner 931.2.ca.a ✓ 3276
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
931.2.ca.a ✓ 3276 1.a even 1 1 trivial
931.2.ca.a ✓ 3276 931.ca even 63 1 inner
931.2.cb.a yes 3276 19.e even 9 1
931.2.cb.a yes 3276 49.g even 21 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(931, [\chi])\).