Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,14,Mod(28,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.28");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.b (of order \(2\), degree \(1\), 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: | \(31.0969693961\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
28.1 | − | 172.131i | 162.472i | −21436.9 | −30311.5 | 27966.4 | −275351. | 2.27986e6i | 1.56793e6 | 5.21754e6i | |||||||||||||||||
28.2 | − | 170.335i | − | 2487.01i | −20822.1 | −14654.1 | −423626. | 377681. | 2.15135e6i | −4.59090e6 | 2.49611e6i | ||||||||||||||||
28.3 | − | 162.205i | 2079.21i | −18118.4 | 28499.1 | 337258. | 310872. | 1.61011e6i | −2.72878e6 | − | 4.62269e6i | ||||||||||||||||
28.4 | − | 150.378i | − | 424.630i | −14421.4 | 51875.3 | −63854.8 | −9683.03 | 936765.i | 1.41401e6 | − | 7.80089e6i | |||||||||||||||
28.5 | − | 132.025i | 277.645i | −9238.68 | −56763.6 | 36656.1 | 461874. | 138188.i | 1.51724e6 | 7.49423e6i | |||||||||||||||||
28.6 | − | 126.947i | 1277.29i | −7923.52 | −10445.6 | 162148. | −142325. | − | 34082.3i | −37154.7 | 1.32604e6i | ||||||||||||||||
28.7 | − | 126.142i | − | 1441.05i | −7719.68 | 18388.4 | −181776. | −251905. | − | 59579.3i | −482306. | − | 2.31954e6i | ||||||||||||||
28.8 | − | 98.6070i | − | 1104.52i | −1531.33 | −7305.52 | −108914. | 327252. | − | 656788.i | 374351. | 720375.i | |||||||||||||||
28.9 | − | 98.5448i | 1929.16i | −1519.09 | −5197.51 | 190109. | −337055. | − | 657581.i | −2.12734e6 | 512188.i | ||||||||||||||||
28.10 | − | 93.2678i | − | 1663.21i | −506.883 | −63620.5 | −155124. | −566395. | − | 716774.i | −1.17195e6 | 5.93374e6i | |||||||||||||||
28.11 | − | 67.0223i | 954.542i | 3700.01 | 48346.3 | 63975.5 | 444756. | − | 797030.i | 683173. | − | 3.24028e6i | |||||||||||||||
28.12 | − | 53.0296i | 485.442i | 5379.86 | 48264.8 | 25742.8 | −490607. | − | 719711.i | 1.35867e6 | − | 2.55946e6i | |||||||||||||||
28.13 | − | 36.6487i | 2214.40i | 6848.87 | −60644.2 | 81155.0 | 368083. | − | 551229.i | −3.30925e6 | 2.22253e6i | ||||||||||||||||
28.14 | − | 33.2848i | − | 1160.53i | 7084.12 | −2193.20 | −38628.1 | 222431. | − | 508463.i | 247490. | 73000.2i | |||||||||||||||
28.15 | − | 32.2136i | 483.965i | 7154.29 | −28573.6 | 15590.2 | −142510. | − | 494358.i | 1.36010e6 | 920457.i | ||||||||||||||||
28.16 | − | 28.9666i | − | 2232.02i | 7352.94 | 38938.5 | −64654.1 | −97987.5 | − | 450284.i | −3.38761e6 | − | 1.12791e6i | ||||||||||||||
28.17 | 28.9666i | 2232.02i | 7352.94 | 38938.5 | −64654.1 | −97987.5 | 450284.i | −3.38761e6 | 1.12791e6i | ||||||||||||||||||
28.18 | 32.2136i | − | 483.965i | 7154.29 | −28573.6 | 15590.2 | −142510. | 494358.i | 1.36010e6 | − | 920457.i | ||||||||||||||||
28.19 | 33.2848i | 1160.53i | 7084.12 | −2193.20 | −38628.1 | 222431. | 508463.i | 247490. | − | 73000.2i | |||||||||||||||||
28.20 | 36.6487i | − | 2214.40i | 6848.87 | −60644.2 | 81155.0 | 368083. | 551229.i | −3.30925e6 | − | 2.22253e6i | ||||||||||||||||
See all 32 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
29.b | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 29.14.b.a | ✓ | 32 |
29.b | even | 2 | 1 | inner | 29.14.b.a | ✓ | 32 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
29.14.b.a | ✓ | 32 | 1.a | even | 1 | 1 | trivial |
29.14.b.a | ✓ | 32 | 29.b | even | 2 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{14}^{\mathrm{new}}(29, [\chi])\).