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Properties

Label 22.14.c.b
Level $22$
Weight $14$
Character orbit 22.c
Analytic conductor $23.591$
Analytic rank $0$
Dimension $28$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [22,14,Mod(3,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.3");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 22.c (of order \(5\), 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: \(23.5908043694\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 448 q^{2} - 1248 q^{3} - 28672 q^{4} + 71554 q^{5} + 99008 q^{6} + 361734 q^{7} - 1835008 q^{8} - 8615367 q^{9} + 2898176 q^{10} + 8699239 q^{11} - 2449408 q^{12} + 32373940 q^{13} + 23150976 q^{14}+ \cdots + 71382923151637 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
3.1 −51.7771 + 37.6183i −675.486 − 2078.93i 1265.73 − 3895.53i −36563.1 − 26564.6i 113181. + 82230.5i −161776. + 497897.i 81007.0 + 249314.i −2.57584e6 + 1.87146e6i 2.89245e6
3.2 −51.7771 + 37.6183i −630.449 − 1940.32i 1265.73 − 3895.53i 52985.6 + 38496.3i 105634. + 76747.8i 86177.6 − 265227.i 81007.0 + 249314.i −2.07755e6 + 1.50943e6i −4.19160e6
3.3 −51.7771 + 37.6183i −365.266 − 1124.17i 1265.73 − 3895.53i −21575.3 − 15675.4i 61201.8 + 44465.7i 145958. − 449212.i 81007.0 + 249314.i 159488. − 115875.i 1.70679e6
3.4 −51.7771 + 37.6183i 41.6348 + 128.139i 1265.73 − 3895.53i 2573.60 + 1869.83i −6976.08 − 5068.42i −27076.8 + 83333.8i 81007.0 + 249314.i 1.27515e6 − 926449.i −203593.
3.5 −51.7771 + 37.6183i 226.298 + 696.474i 1265.73 − 3895.53i 39506.7 + 28703.3i −37917.2 − 27548.5i −100433. + 309100.i 81007.0 + 249314.i 855969. − 621898.i −3.12531e6
3.6 −51.7771 + 37.6183i 412.870 + 1270.68i 1265.73 − 3895.53i −41240.7 − 29963.1i −69178.0 − 50260.8i 25390.0 − 78142.3i 81007.0 + 249314.i −154338. + 112133.i 3.26248e6
3.7 −51.7771 + 37.6183i 751.070 + 2311.56i 1265.73 − 3895.53i 25138.8 + 18264.4i −125845. − 91431.7i 81934.7 − 252169.i 81007.0 + 249314.i −3.48935e6 + 2.53516e6i −1.98869e6
5.1 19.7771 + 60.8676i −2003.44 − 1455.58i −3313.73 + 2407.57i 12586.7 − 38738.0i 48975.7 − 150732.i 345957. − 251352.i −212079. − 154084.i 1.40237e6 + 4.31604e6i 2.60682e6
5.2 19.7771 + 60.8676i −1229.94 − 893.604i −3313.73 + 2407.57i −7708.37 + 23723.9i 30066.9 − 92536.4i −267598. + 194422.i −212079. − 154084.i 221552. + 681866.i −1.59647e6
5.3 19.7771 + 60.8676i −501.424 − 364.306i −3313.73 + 2407.57i 17458.1 − 53730.4i 12257.7 − 37725.4i −385628. + 280175.i −212079. − 154084.i −373966. − 1.15095e6i 3.61571e6
5.4 19.7771 + 60.8676i −306.982 − 223.036i −3313.73 + 2407.57i −5178.33 + 15937.3i 7504.43 − 23096.3i 291527. − 211807.i −212079. − 154084.i −448180. − 1.37936e6i −1.07248e6
5.5 19.7771 + 60.8676i 697.531 + 506.786i −3313.73 + 2407.57i 7802.80 − 24014.5i −17051.7 + 52479.8i 9628.39 − 6995.43i −212079. − 154084.i −262955. − 809293.i 1.61602e6
5.6 19.7771 + 60.8676i 1193.16 + 866.884i −3313.73 + 2407.57i −16233.3 + 49960.9i −29167.9 + 89769.5i −203084. + 147550.i −212079. − 154084.i 179478. + 552378.i −3.36205e6
5.7 19.7771 + 60.8676i 1766.42 + 1283.38i −3313.73 + 2407.57i 6223.79 − 19154.8i −43181.5 + 132899.i 339891. − 246945.i −212079. − 154084.i 980497. + 3.01766e6i 1.28900e6
9.1 19.7771 − 60.8676i −2003.44 + 1455.58i −3313.73 − 2407.57i 12586.7 + 38738.0i 48975.7 + 150732.i 345957. + 251352.i −212079. + 154084.i 1.40237e6 − 4.31604e6i 2.60682e6
9.2 19.7771 − 60.8676i −1229.94 + 893.604i −3313.73 − 2407.57i −7708.37 − 23723.9i 30066.9 + 92536.4i −267598. − 194422.i −212079. + 154084.i 221552. − 681866.i −1.59647e6
9.3 19.7771 − 60.8676i −501.424 + 364.306i −3313.73 − 2407.57i 17458.1 + 53730.4i 12257.7 + 37725.4i −385628. − 280175.i −212079. + 154084.i −373966. + 1.15095e6i 3.61571e6
9.4 19.7771 − 60.8676i −306.982 + 223.036i −3313.73 − 2407.57i −5178.33 − 15937.3i 7504.43 + 23096.3i 291527. + 211807.i −212079. + 154084.i −448180. + 1.37936e6i −1.07248e6
9.5 19.7771 − 60.8676i 697.531 − 506.786i −3313.73 − 2407.57i 7802.80 + 24014.5i −17051.7 − 52479.8i 9628.39 + 6995.43i −212079. + 154084.i −262955. + 809293.i 1.61602e6
9.6 19.7771 − 60.8676i 1193.16 − 866.884i −3313.73 − 2407.57i −16233.3 − 49960.9i −29167.9 − 89769.5i −203084. − 147550.i −212079. + 154084.i 179478. − 552378.i −3.36205e6
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3.7
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 22.14.c.b ✓ 28
11.c even 5 1 inner 22.14.c.b ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
22.14.c.b ✓ 28 1.a even 1 1 trivial
22.14.c.b ✓ 28 11.c even 5 1 inner