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Properties

Label 1295.2.j.a
Level $1295$
Weight $2$
Character orbit 1295.j
Analytic conductor $10.341$
Analytic rank $0$
Dimension $38$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1295,2,Mod(186,1295)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1295, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1295.186"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1295 = 5 \cdot 7 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1295.j (of order \(3\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [38] 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: \(10.3406270618\)
Analytic rank: \(0\)
Dimension: \(38\)
Relative dimension: \(19\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
186.1 −1.20852 − 2.09322i −0.326680 + 0.565827i −1.92105 + 3.32736i −0.500000 − 0.866025i 1.57920 −2.27698 − 1.34736i 4.45245 1.28656 + 2.22839i −1.20852 + 2.09322i
186.2 −1.02244 − 1.77091i 0.873855 − 1.51356i −1.09075 + 1.88924i −0.500000 − 0.866025i −3.57384 1.83604 + 1.90498i 0.371155 −0.0272447 − 0.0471893i −1.02244 + 1.77091i
186.3 −0.966124 − 1.67338i 1.39627 − 2.41841i −0.866792 + 1.50133i −0.500000 − 0.866025i −5.39588 −1.04689 − 2.42982i −0.514782 −2.39913 − 4.15542i −0.966124 + 1.67338i
186.4 −0.845611 − 1.46464i −1.04410 + 1.80844i −0.430116 + 0.744982i −0.500000 − 0.866025i 3.53162 2.57439 + 0.610338i −1.92760 −0.680306 − 1.17832i −0.845611 + 1.46464i
186.5 −0.597934 − 1.03565i −1.20438 + 2.08605i 0.284950 − 0.493547i −0.500000 − 0.866025i 2.88056 −1.59963 + 2.10741i −3.07326 −1.40107 − 2.42672i −0.597934 + 1.03565i
186.6 −0.594239 − 1.02925i −0.227438 + 0.393934i 0.293760 − 0.508808i −0.500000 − 0.866025i 0.540610 0.915835 − 2.48219i −3.07521 1.39654 + 2.41888i −0.594239 + 1.02925i
186.7 −0.439861 − 0.761862i 0.702103 − 1.21608i 0.613044 − 1.06182i −0.500000 − 0.866025i −1.23531 −1.97238 − 1.76344i −2.83806 0.514102 + 0.890450i −0.439861 + 0.761862i
186.8 −0.303694 − 0.526013i 0.192036 − 0.332615i 0.815540 − 1.41256i −0.500000 − 0.866025i −0.233280 1.01512 + 2.44326i −2.20547 1.42624 + 2.47033i −0.303694 + 0.526013i
186.9 −0.0342024 − 0.0592404i 1.52426 − 2.64010i 0.997660 − 1.72800i −0.500000 − 0.866025i −0.208534 −2.27935 + 1.34334i −0.273299 −3.14677 − 5.45036i −0.0342024 + 0.0592404i
186.10 0.189789 + 0.328725i −0.313780 + 0.543483i 0.927960 − 1.60727i −0.500000 − 0.866025i −0.238209 −2.24021 + 1.40764i 1.46363 1.30308 + 2.25701i 0.189789 − 0.328725i
186.11 0.306680 + 0.531185i −0.923254 + 1.59912i 0.811895 − 1.40624i −0.500000 − 0.866025i −1.13257 2.55098 − 0.701777i 2.22269 −0.204795 − 0.354715i 0.306680 − 0.531185i
186.12 0.357733 + 0.619611i 0.00692605 − 0.0119963i 0.744055 − 1.28874i −0.500000 − 0.866025i 0.00991070 2.33024 − 1.25300i 2.49562 1.49990 + 2.59791i 0.357733 − 0.619611i
186.13 0.458759 + 0.794593i 1.13848 − 1.97191i 0.579081 − 1.00300i −0.500000 − 0.866025i 2.08916 2.28132 + 1.33999i 2.89767 −1.09229 − 1.89191i 0.458759 − 0.794593i
186.14 0.801447 + 1.38815i −1.11974 + 1.93944i −0.284634 + 0.493001i −0.500000 − 0.866025i −3.58964 −0.281235 + 2.63076i 2.29331 −1.00763 − 1.74526i 0.801447 − 1.38815i
186.15 0.823521 + 1.42638i −0.748028 + 1.29562i −0.356373 + 0.617257i −0.500000 − 0.866025i −2.46407 −2.52327 − 0.795673i 2.12016 0.380910 + 0.659755i 0.823521 − 1.42638i
186.16 0.983510 + 1.70349i −1.61976 + 2.80550i −0.934584 + 1.61875i −0.500000 − 0.866025i −6.37219 0.615110 − 2.57325i 0.257349 −3.74723 − 6.49039i 0.983510 − 1.70349i
186.17 1.04486 + 1.80975i 1.31471 − 2.27715i −1.18346 + 2.04981i −0.500000 − 0.866025i 5.49475 2.32516 − 1.26238i −0.766757 −1.95693 − 3.38951i 1.04486 − 1.80975i
186.18 1.20914 + 2.09428i 0.744284 − 1.28914i −1.92402 + 3.33249i −0.500000 − 0.866025i 3.59976 −1.93133 − 1.80831i −4.46904 0.392084 + 0.679110i 1.20914 − 2.09428i
186.19 1.33719 + 2.31608i 0.134228 − 0.232489i −2.57617 + 4.46205i −0.500000 − 0.866025i 0.717953 −0.292931 + 2.62948i −8.43054 1.46397 + 2.53566i 1.33719 − 2.31608i
926.1 −1.20852 + 2.09322i −0.326680 − 0.565827i −1.92105 − 3.32736i −0.500000 + 0.866025i 1.57920 −2.27698 + 1.34736i 4.45245 1.28656 − 2.22839i −1.20852 − 2.09322i
See all 38 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 186.19
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1295.2.j.a ✓ 38
7.c even 3 1 inner 1295.2.j.a ✓ 38
7.c even 3 1 9065.2.a.r 19
7.d odd 6 1 9065.2.a.s 19
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1295.2.j.a ✓ 38 1.a even 1 1 trivial
1295.2.j.a ✓ 38 7.c even 3 1 inner
9065.2.a.r 19 7.c even 3 1
9065.2.a.s 19 7.d odd 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{38} - 3 T_{2}^{37} + 29 T_{2}^{36} - 64 T_{2}^{35} + 425 T_{2}^{34} - 796 T_{2}^{33} + 4158 T_{2}^{32} + \cdots + 81 \) acting on \(S_{2}^{\mathrm{new}}(1295, [\chi])\). Copy content Toggle raw display