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Properties

Label 790.2.m.c
Level $790$
Weight $2$
Character orbit 790.m
Analytic conductor $6.308$
Analytic rank $0$
Dimension $48$
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [790,2,Mod(21,790)] 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("790.21"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(790, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([0, 18])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 790 = 2 \cdot 5 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 790.m (of order \(13\), degree \(12\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48,4,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.30818175968\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{13})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{13}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 4 q^{2} - q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 9 q^{7} + 4 q^{8} - 21 q^{9} + 4 q^{10} + 2 q^{11} - q^{12} + 17 q^{13} - 4 q^{14} - 14 q^{15} - 4 q^{16} - 6 q^{17} + 21 q^{18} - 34 q^{19} - 4 q^{20}+ \cdots - 99 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
21.1 0.748511 − 0.663123i −0.965499 + 1.39877i 0.120537 − 0.992709i −0.970942 + 0.239316i 0.204868 + 1.68724i −1.42706 + 2.06746i −0.568065 − 0.822984i 0.0394546 + 0.104033i −0.568065 + 0.822984i
21.2 0.748511 − 0.663123i 0.161159 − 0.233479i 0.120537 − 0.992709i −0.970942 + 0.239316i −0.0341960 − 0.281630i −1.65882 + 2.40321i −0.568065 − 0.822984i 1.03527 + 2.72979i −0.568065 + 0.822984i
21.3 0.748511 − 0.663123i 1.09143 − 1.58121i 0.120537 − 0.992709i −0.970942 + 0.239316i −0.231588 − 1.90730i 2.75688 − 3.99403i −0.568065 − 0.822984i −0.245184 − 0.646496i −0.568065 + 0.822984i
21.4 0.748511 − 0.663123i 1.68985 − 2.44817i 0.120537 − 0.992709i −0.970942 + 0.239316i −0.358566 − 2.95305i −0.752285 + 1.08987i −0.568065 − 0.822984i −2.07412 − 5.46900i −0.568065 + 0.822984i
101.1 −0.568065 + 0.822984i −1.96396 + 0.484072i −0.354605 − 0.935016i −0.748511 − 0.663123i 0.717272 − 1.89129i −3.91903 + 0.965954i 0.970942 + 0.239316i 0.966439 − 0.507226i 0.970942 − 0.239316i
101.2 −0.568065 + 0.822984i 0.0777728 − 0.0191693i −0.354605 − 0.935016i −0.748511 − 0.663123i −0.0284040 + 0.0748952i 3.25987 − 0.803487i 0.970942 + 0.239316i −2.65069 + 1.39119i 0.970942 − 0.239316i
101.3 −0.568065 + 0.822984i 0.608287 − 0.149929i −0.354605 − 0.935016i −0.748511 − 0.663123i −0.222157 + 0.585780i −0.570841 + 0.140700i 0.970942 + 0.239316i −2.30883 + 1.21177i 0.970942 − 0.239316i
101.4 −0.568065 + 0.822984i 1.79234 − 0.441772i −0.354605 − 0.935016i −0.748511 − 0.663123i −0.654594 + 1.72602i −1.88655 + 0.464993i 0.970942 + 0.239316i 0.360955 − 0.189444i 0.970942 − 0.239316i
131.1 −0.885456 − 0.464723i −0.319628 + 2.63238i 0.568065 + 0.822984i −0.354605 − 0.935016i 1.50634 − 2.18231i 0.338375 − 2.78677i −0.120537 − 0.992709i −3.91442 − 0.964817i −0.120537 + 0.992709i
131.2 −0.885456 − 0.464723i −0.0730245 + 0.601411i 0.568065 + 0.822984i −0.354605 − 0.935016i 0.344149 − 0.498586i −0.485731 + 4.00035i −0.120537 − 0.992709i 2.55646 + 0.630112i −0.120537 + 0.992709i
131.3 −0.885456 − 0.464723i 0.166135 − 1.36824i 0.568065 + 0.822984i −0.354605 − 0.935016i −0.782959 + 1.13431i −0.164771 + 1.35702i −0.120537 − 0.992709i 1.06834 + 0.263321i −0.120537 + 0.992709i
131.4 −0.885456 − 0.464723i 0.400677 − 3.29987i 0.568065 + 0.822984i −0.354605 − 0.935016i −1.88831 + 2.73569i −0.106587 + 0.877823i −0.120537 − 0.992709i −7.81578 − 1.92642i −0.120537 + 0.992709i
141.1 0.970942 + 0.239316i −2.41490 + 2.13941i 0.885456 + 0.464723i 0.568065 − 0.822984i −2.85672 + 1.49932i 1.36211 − 1.20673i 0.748511 + 0.663123i 0.893037 − 7.35482i 0.748511 − 0.663123i
141.2 0.970942 + 0.239316i 0.0574854 − 0.0509276i 0.885456 + 0.464723i 0.568065 − 0.822984i 0.0680027 − 0.0356906i 1.82715 − 1.61872i 0.748511 + 0.663123i −0.360899 + 2.97227i 0.748511 − 0.663123i
141.3 0.970942 + 0.239316i 0.589522 − 0.522271i 0.885456 + 0.464723i 0.568065 − 0.822984i 0.697380 − 0.366013i −3.19730 + 2.83256i 0.748511 + 0.663123i −0.286841 + 2.36235i 0.748511 − 0.663123i
141.4 0.970942 + 0.239316i 1.73068 − 1.53325i 0.885456 + 0.464723i 0.568065 − 0.822984i 2.04732 − 1.07452i 1.05448 − 0.934183i 0.748511 + 0.663123i 0.282791 − 2.32899i 0.748511 − 0.663123i
301.1 0.748511 + 0.663123i −0.965499 − 1.39877i 0.120537 + 0.992709i −0.970942 − 0.239316i 0.204868 − 1.68724i −1.42706 − 2.06746i −0.568065 + 0.822984i 0.0394546 − 0.104033i −0.568065 − 0.822984i
301.2 0.748511 + 0.663123i 0.161159 + 0.233479i 0.120537 + 0.992709i −0.970942 − 0.239316i −0.0341960 + 0.281630i −1.65882 − 2.40321i −0.568065 + 0.822984i 1.03527 − 2.72979i −0.568065 − 0.822984i
301.3 0.748511 + 0.663123i 1.09143 + 1.58121i 0.120537 + 0.992709i −0.970942 − 0.239316i −0.231588 + 1.90730i 2.75688 + 3.99403i −0.568065 + 0.822984i −0.245184 + 0.646496i −0.568065 − 0.822984i
301.4 0.748511 + 0.663123i 1.68985 + 2.44817i 0.120537 + 0.992709i −0.970942 − 0.239316i −0.358566 + 2.95305i −0.752285 − 1.08987i −0.568065 + 0.822984i −2.07412 + 5.46900i −0.568065 − 0.822984i
See all 48 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 21.4
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
79.e even 13 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 790.2.m.c ✓ 48
79.e even 13 1 inner 790.2.m.c ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
790.2.m.c ✓ 48 1.a even 1 1 trivial
790.2.m.c ✓ 48 79.e even 13 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{48} + T_{3}^{47} + 17 T_{3}^{46} + 18 T_{3}^{45} + 182 T_{3}^{44} + 148 T_{3}^{43} + 1950 T_{3}^{42} + \cdots + 17161 \) acting on \(S_{2}^{\mathrm{new}}(790, [\chi])\). Copy content Toggle raw display