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: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3.1 | 51.7771 | − | 37.6183i | −663.076 | − | 2040.74i | 1265.73 | − | 3895.53i | 18873.2 | + | 13712.2i | −111101. | − | 80719.7i | −130921. | + | 402934.i | −81007.0 | − | 249314.i | −2.43511e6 | + | 1.76921e6i | 1.49303e6 | ||
3.2 | 51.7771 | − | 37.6183i | −417.662 | − | 1285.43i | 1265.73 | − | 3895.53i | −34004.8 | − | 24705.9i | −69981.0 | − | 50844.2i | 96600.4 | − | 297306.i | −81007.0 | − | 249314.i | −188057. | + | 136631.i | −2.69006e6 | ||
3.3 | 51.7771 | − | 37.6183i | −252.702 | − | 777.736i | 1265.73 | − | 3895.53i | 25133.6 | + | 18260.6i | −42341.2 | − | 30762.7i | 29224.9 | − | 89945.0i | −81007.0 | − | 249314.i | 748819. | − | 544049.i | 1.98828e6 | ||
3.4 | 51.7771 | − | 37.6183i | 346.581 | + | 1066.67i | 1265.73 | − | 3895.53i | −24923.9 | − | 18108.3i | 58071.1 | + | 42191.1i | −7979.10 | + | 24557.2i | −81007.0 | − | 249314.i | 272175. | − | 197747.i | −1.97169e6 | ||
3.5 | 51.7771 | − | 37.6183i | 460.202 | + | 1416.35i | 1265.73 | − | 3895.53i | 46818.1 | + | 34015.4i | 77108.7 | + | 56022.7i | −157481. | + | 484676.i | −81007.0 | − | 249314.i | −504441. | + | 366498.i | 3.70370e6 | ||
3.6 | 51.7771 | − | 37.6183i | 461.283 | + | 1419.68i | 1265.73 | − | 3895.53i | −3259.92 | − | 2368.47i | 77289.8 | + | 56154.3i | 80603.6 | − | 248072.i | −81007.0 | − | 249314.i | −512880. | + | 372629.i | −257887. | ||
5.1 | −19.7771 | − | 60.8676i | −1602.93 | − | 1164.60i | −3313.73 | + | 2407.57i | 100.214 | − | 308.427i | −39185.0 | + | 120599.i | 51623.9 | − | 37507.0i | 212079. | + | 154084.i | 720428. | + | 2.21725e6i | −20755.1 | ||
5.2 | −19.7771 | − | 60.8676i | −351.775 | − | 255.580i | −3313.73 | + | 2407.57i | −3087.88 | + | 9503.52i | −8599.44 | + | 26466.3i | 327454. | − | 237910.i | 212079. | + | 154084.i | −434248. | − | 1.33648e6i | 639526. | ||
5.3 | −19.7771 | − | 60.8676i | −269.653 | − | 195.914i | −3313.73 | + | 2407.57i | −21195.1 | + | 65231.8i | −6591.88 | + | 20287.7i | −348859. | + | 253461.i | 212079. | + | 154084.i | −458343. | − | 1.41063e6i | 4.38968e6 | ||
5.4 | −19.7771 | − | 60.8676i | 719.209 | + | 522.536i | −3313.73 | + | 2407.57i | 552.241 | − | 1699.62i | 17581.7 | − | 54110.8i | −85138.9 | + | 61857.0i | 212079. | + | 154084.i | −248455. | − | 764667.i | −114374. | ||
5.5 | −19.7771 | − | 60.8676i | 950.343 | + | 690.465i | −3313.73 | + | 2407.57i | 20485.5 | − | 63047.8i | 23231.9 | − | 71500.5i | 4712.51 | − | 3423.84i | 212079. | + | 154084.i | −66262.0 | − | 203934.i | −4.24271e6 | ||
5.6 | −19.7771 | − | 60.8676i | 1974.18 | + | 1434.33i | −3313.73 | + | 2407.57i | −9031.32 | + | 27795.5i | 48260.5 | − | 148531.i | −114626. | + | 83280.8i | 212079. | + | 154084.i | 1.34743e6 | + | 4.14695e6i | 1.87046e6 | ||
9.1 | −19.7771 | + | 60.8676i | −1602.93 | + | 1164.60i | −3313.73 | − | 2407.57i | 100.214 | + | 308.427i | −39185.0 | − | 120599.i | 51623.9 | + | 37507.0i | 212079. | − | 154084.i | 720428. | − | 2.21725e6i | −20755.1 | ||
9.2 | −19.7771 | + | 60.8676i | −351.775 | + | 255.580i | −3313.73 | − | 2407.57i | −3087.88 | − | 9503.52i | −8599.44 | − | 26466.3i | 327454. | + | 237910.i | 212079. | − | 154084.i | −434248. | + | 1.33648e6i | 639526. | ||
9.3 | −19.7771 | + | 60.8676i | −269.653 | + | 195.914i | −3313.73 | − | 2407.57i | −21195.1 | − | 65231.8i | −6591.88 | − | 20287.7i | −348859. | − | 253461.i | 212079. | − | 154084.i | −458343. | + | 1.41063e6i | 4.38968e6 | ||
9.4 | −19.7771 | + | 60.8676i | 719.209 | − | 522.536i | −3313.73 | − | 2407.57i | 552.241 | + | 1699.62i | 17581.7 | + | 54110.8i | −85138.9 | − | 61857.0i | 212079. | − | 154084.i | −248455. | + | 764667.i | −114374. | ||
9.5 | −19.7771 | + | 60.8676i | 950.343 | − | 690.465i | −3313.73 | − | 2407.57i | 20485.5 | + | 63047.8i | 23231.9 | + | 71500.5i | 4712.51 | + | 3423.84i | 212079. | − | 154084.i | −66262.0 | + | 203934.i | −4.24271e6 | ||
9.6 | −19.7771 | + | 60.8676i | 1974.18 | − | 1434.33i | −3313.73 | − | 2407.57i | −9031.32 | − | 27795.5i | 48260.5 | + | 148531.i | −114626. | − | 83280.8i | 212079. | − | 154084.i | 1.34743e6 | − | 4.14695e6i | 1.87046e6 | ||
15.1 | 51.7771 | + | 37.6183i | −663.076 | + | 2040.74i | 1265.73 | + | 3895.53i | 18873.2 | − | 13712.2i | −111101. | + | 80719.7i | −130921. | − | 402934.i | −81007.0 | + | 249314.i | −2.43511e6 | − | 1.76921e6i | 1.49303e6 | ||
15.2 | 51.7771 | + | 37.6183i | −417.662 | + | 1285.43i | 1265.73 | + | 3895.53i | −34004.8 | + | 24705.9i | −69981.0 | + | 50844.2i | 96600.4 | + | 297306.i | −81007.0 | + | 249314.i | −188057. | − | 136631.i | −2.69006e6 | ||
See all 24 embeddings |
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.a | ✓ | 24 |
11.c | even | 5 | 1 | inner | 22.14.c.a | ✓ | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
22.14.c.a | ✓ | 24 | 1.a | even | 1 | 1 | trivial |
22.14.c.a | ✓ | 24 | 11.c | even | 5 | 1 | inner |