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Properties

Label 931.2.v.e
Level $931$
Weight $2$
Character orbit 931.v
Analytic conductor $7.434$
Analytic rank $0$
Dimension $30$
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(177,931)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(931, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([6, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("931.177");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.v (of order \(9\), degree \(6\), not 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: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 133)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 30 q + 3 q^{3} + 12 q^{4} - 3 q^{5} + 9 q^{6} + 9 q^{8} - 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 30 q + 3 q^{3} + 12 q^{4} - 3 q^{5} + 9 q^{6} + 9 q^{8} - 21 q^{9} - 36 q^{10} - 18 q^{12} - 30 q^{15} + 15 q^{17} + 15 q^{18} - 6 q^{19} + 30 q^{20} + 12 q^{22} + 12 q^{23} + 63 q^{24} + 21 q^{25} + 45 q^{26} - 27 q^{27} - 42 q^{30} + 24 q^{31} + 60 q^{32} - 9 q^{33} + 42 q^{34} - 21 q^{36} + 18 q^{37} + 60 q^{38} + 12 q^{39} - 87 q^{40} - 3 q^{41} - 12 q^{43} - 72 q^{44} + 54 q^{45} + 6 q^{46} + 36 q^{47} - 18 q^{48} - 3 q^{50} + 15 q^{52} - 15 q^{53} + 21 q^{54} - 33 q^{55} - 12 q^{57} + 30 q^{58} - 42 q^{59} + 12 q^{60} + 75 q^{61} - 96 q^{62} + 3 q^{64} - 90 q^{65} - 18 q^{66} + 30 q^{67} + 102 q^{68} - 15 q^{69} + 30 q^{71} + 99 q^{72} + 12 q^{73} - 57 q^{74} - 72 q^{75} - 84 q^{76} + 6 q^{78} + 3 q^{79} - 78 q^{80} - 6 q^{81} + 6 q^{82} - 12 q^{83} + 42 q^{85} + 42 q^{86} - 24 q^{87} - 72 q^{88} - 24 q^{89} - 180 q^{90} - 75 q^{92} + 12 q^{93} - 21 q^{94} + 30 q^{95} + 33 q^{96} + 63 q^{97} + 45 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
177.1 −0.361926 − 2.05258i −0.505259 − 2.86547i −2.20273 + 0.801727i 0.234951 + 0.0855151i −5.69875 + 2.07417i 0 0.358588 + 0.621093i −5.13654 + 1.86955i 0.0904922 − 0.513206i
177.2 −0.295006 − 1.67306i 0.530064 + 3.00614i −0.832714 + 0.303083i 1.21755 + 0.443151i 4.87308 − 1.77366i 0 −0.946138 − 1.63876i −5.93684 + 2.16083i 0.382235 − 2.16776i
177.3 0.0498910 + 0.282946i 0.383114 + 2.17275i 1.80182 − 0.655807i −3.29535 − 1.19941i −0.595656 + 0.216801i 0 0.562764 + 0.974735i −1.75498 + 0.638759i 0.174960 − 0.992247i
177.4 0.105921 + 0.600708i 0.0260769 + 0.147890i 1.52975 − 0.556785i 2.81231 + 1.02360i −0.0860764 + 0.0313292i 0 1.10647 + 1.91647i 2.79789 − 1.01835i −0.317000 + 1.79780i
177.5 0.327471 + 1.85718i −0.352744 − 2.00051i −1.46250 + 0.532308i −2.40915 − 0.876858i 3.59980 − 1.31022i 0 0.418312 + 0.724538i −1.05853 + 0.385273i 0.839558 − 4.76137i
214.1 −1.94839 − 1.63490i 2.31234 + 1.94029i 0.776054 + 4.40122i 0.492064 − 2.79063i −1.33319 − 7.56088i 0 3.14003 − 5.43870i 1.06128 + 6.01879i −5.52113 + 4.63278i
214.2 −1.05191 − 0.882655i −2.01845 − 1.69368i −0.0198673 − 0.112673i −0.0743456 + 0.421635i 0.628286 + 3.56318i 0 −1.45172 + 2.51445i 0.684638 + 3.88278i 0.450363 − 0.377899i
214.3 −0.580759 − 0.487315i 0.965676 + 0.810299i −0.247491 − 1.40359i −0.170576 + 0.967387i −0.165955 − 0.941177i 0 −1.29838 + 2.24887i −0.244998 − 1.38945i 0.570486 − 0.478694i
214.4 1.34511 + 1.12868i 2.15616 + 1.80924i 0.188100 + 1.06677i −0.603238 + 3.42113i 0.858223 + 4.86723i 0 0.804890 − 1.39411i 0.854761 + 4.84759i −4.67277 + 3.92092i
214.5 1.46991 + 1.23340i −0.443955 − 0.372522i 0.292060 + 1.65636i 0.0297440 − 0.168687i −0.193104 − 1.09515i 0 0.305182 − 0.528591i −0.462622 − 2.62366i 0.251779 − 0.211268i
263.1 −0.361926 + 2.05258i −0.505259 + 2.86547i −2.20273 − 0.801727i 0.234951 − 0.0855151i −5.69875 − 2.07417i 0 0.358588 − 0.621093i −5.13654 − 1.86955i 0.0904922 + 0.513206i
263.2 −0.295006 + 1.67306i 0.530064 − 3.00614i −0.832714 − 0.303083i 1.21755 − 0.443151i 4.87308 + 1.77366i 0 −0.946138 + 1.63876i −5.93684 − 2.16083i 0.382235 + 2.16776i
263.3 0.0498910 − 0.282946i 0.383114 − 2.17275i 1.80182 + 0.655807i −3.29535 + 1.19941i −0.595656 − 0.216801i 0 0.562764 − 0.974735i −1.75498 − 0.638759i 0.174960 + 0.992247i
263.4 0.105921 − 0.600708i 0.0260769 − 0.147890i 1.52975 + 0.556785i 2.81231 − 1.02360i −0.0860764 − 0.0313292i 0 1.10647 − 1.91647i 2.79789 + 1.01835i −0.317000 − 1.79780i
263.5 0.327471 − 1.85718i −0.352744 + 2.00051i −1.46250 − 0.532308i −2.40915 + 0.876858i 3.59980 + 1.31022i 0 0.418312 − 0.724538i −1.05853 − 0.385273i 0.839558 + 4.76137i
275.1 −2.15877 − 0.785729i −2.84007 − 1.03370i 2.51084 + 2.10685i 2.40965 − 2.02194i 5.31886 + 4.46305i 0 −1.46761 − 2.54197i 4.69933 + 3.94321i −6.79058 + 2.47157i
275.2 −1.52863 − 0.556375i 1.01101 + 0.367976i 0.495058 + 0.415403i −0.0539084 + 0.0452345i −1.34072 − 1.12500i 0 1.10109 + 1.90715i −1.41140 − 1.18431i 0.107573 − 0.0391534i
275.3 0.593576 + 0.216044i 1.40700 + 0.512107i −1.22643 − 1.02910i −2.76219 + 2.31776i 0.724525 + 0.607949i 0 −1.13732 − 1.96990i −0.580731 − 0.487291i −2.14031 + 0.779008i
275.4 1.53348 + 0.558142i −0.433596 − 0.157816i 0.507958 + 0.426227i 2.86936 − 2.40768i −0.576829 − 0.484017i 0 −1.09085 − 1.88941i −2.13503 − 1.79151i 5.74394 − 2.09062i
275.5 2.50003 + 0.909938i −0.697375 − 0.253824i 3.89009 + 3.26418i −2.19686 + 1.84339i −1.51250 − 1.26914i 0 4.09469 + 7.09220i −1.87623 − 1.57434i −7.16960 + 2.60952i
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 177.5
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
133.u even 9 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 931.2.v.e 30
7.b odd 2 1 931.2.v.d 30
7.c even 3 1 931.2.w.b 30
7.c even 3 1 931.2.x.d 30
7.d odd 6 1 133.2.v.b ✓ 30
7.d odd 6 1 931.2.x.e 30
19.e even 9 1 931.2.x.d 30
133.u even 9 1 inner 931.2.v.e 30
133.w even 9 1 931.2.w.b 30
133.x odd 18 1 931.2.v.d 30
133.x odd 18 1 2527.2.a.r 15
133.y odd 18 1 931.2.x.e 30
133.z odd 18 1 133.2.v.b ✓ 30
133.bb even 18 1 2527.2.a.s 15
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
133.2.v.b ✓ 30 7.d odd 6 1
133.2.v.b ✓ 30 133.z odd 18 1
931.2.v.d 30 7.b odd 2 1
931.2.v.d 30 133.x odd 18 1
931.2.v.e 30 1.a even 1 1 trivial
931.2.v.e 30 133.u even 9 1 inner
931.2.w.b 30 7.c even 3 1
931.2.w.b 30 133.w even 9 1
931.2.x.d 30 7.c even 3 1
931.2.x.d 30 19.e even 9 1
931.2.x.e 30 7.d odd 6 1
931.2.x.e 30 133.y odd 18 1
2527.2.a.r 15 133.x odd 18 1
2527.2.a.s 15 133.bb even 18 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(931, [\chi])\):

\( T_{2}^{30} - 6 T_{2}^{28} - 7 T_{2}^{27} + 27 T_{2}^{26} + 30 T_{2}^{25} + 109 T_{2}^{24} + 9 T_{2}^{23} + \cdots + 11449 \) Copy content Toggle raw display
\( T_{3}^{30} - 3 T_{3}^{29} + 15 T_{3}^{28} - 15 T_{3}^{27} + 51 T_{3}^{26} + 150 T_{3}^{25} + \cdots + 26569 \) Copy content Toggle raw display