Properties

Label 35.23.d.a
Level $35$
Weight $23$
Character orbit 35.d
Analytic conductor $107.348$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,23,Mod(6,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 23, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.6");
 
S:= CuspForms(chi, 23);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 23 \)
Character orbit: \([\chi]\) \(=\) 35.d (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: \(107.347602195\)
Analytic rank: \(0\)
Dimension: \(60\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 60 q + 3082 q^{2} + 135428954 q^{4} - 3055909130 q^{7} + 25377678038 q^{8} - 661372200146 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 60 q + 3082 q^{2} + 135428954 q^{4} - 3055909130 q^{7} + 25377678038 q^{8} - 661372200146 q^{9} + 421589555950 q^{11} - 8699235238658 q^{14} - 1566308593750 q^{15} + 369627834003746 q^{16} + 415928127797438 q^{18} - 10\!\cdots\!98 q^{21}+ \cdots - 12\!\cdots\!12 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
6.1 −4050.15 299643.i 1.22094e7 2.18366e7i 1.21360e9i −1.56680e9 + 1.20622e9i −3.24625e10 −5.84046e10 8.84415e10i
6.2 −4050.15 299643.i 1.22094e7 2.18366e7i 1.21360e9i −1.56680e9 1.20622e9i −3.24625e10 −5.84046e10 8.84415e10i
6.3 −3964.42 190565.i 1.15223e7 2.18366e7i 7.55481e8i 1.88278e9 6.04124e8i −2.90514e10 −4.93408e9 8.65695e10i
6.4 −3964.42 190565.i 1.15223e7 2.18366e7i 7.55481e8i 1.88278e9 + 6.04124e8i −2.90514e10 −4.93408e9 8.65695e10i
6.5 −3446.96 82840.2i 7.68724e6 2.18366e7i 2.85547e8i −1.82094e9 + 7.70703e8i −1.20400e10 2.45186e10 7.52699e10i
6.6 −3446.96 82840.2i 7.68724e6 2.18366e7i 2.85547e8i −1.82094e9 7.70703e8i −1.20400e10 2.45186e10 7.52699e10i
6.7 −3172.47 206326.i 5.87023e6 2.18366e7i 6.54561e8i 1.61326e8 + 1.97073e9i −5.31683e9 −1.11893e10 6.92759e10i
6.8 −3172.47 206326.i 5.87023e6 2.18366e7i 6.54561e8i 1.61326e8 1.97073e9i −5.31683e9 −1.11893e10 6.92759e10i
6.9 −2949.79 168176.i 4.50698e6 2.18366e7i 4.96086e8i 1.79437e9 + 8.30701e8i −9.22338e8 3.09777e9 6.44135e10i
6.10 −2949.79 168176.i 4.50698e6 2.18366e7i 4.96086e8i 1.79437e9 8.30701e8i −9.22338e8 3.09777e9 6.44135e10i
6.11 −2940.79 329816.i 4.45397e6 2.18366e7i 9.69921e8i −1.99357e8 1.96725e9i −7.63627e8 −7.73975e10 6.42170e10i
6.12 −2940.79 329816.i 4.45397e6 2.18366e7i 9.69921e8i −1.99357e8 + 1.96725e9i −7.63627e8 −7.73975e10 6.42170e10i
6.13 −2672.32 294572.i 2.94698e6 2.18366e7i 7.87191e8i 1.00290e9 + 1.70411e9i 3.33326e9 −5.53919e10 5.83543e10i
6.14 −2672.32 294572.i 2.94698e6 2.18366e7i 7.87191e8i 1.00290e9 1.70411e9i 3.33326e9 −5.53919e10 5.83543e10i
6.15 −2054.98 104363.i 28626.0 2.18366e7i 2.14463e8i −1.43402e9 1.36139e9i 8.56037e9 2.04895e10 4.48737e10i
6.16 −2054.98 104363.i 28626.0 2.18366e7i 2.14463e8i −1.43402e9 + 1.36139e9i 8.56037e9 2.04895e10 4.48737e10i
6.17 −1882.46 2834.26i −650663. 2.18366e7i 5.33538e6i −7.86883e8 + 1.81401e9i 9.12044e9 3.13730e10 4.11064e10i
6.18 −1882.46 2834.26i −650663. 2.18366e7i 5.33538e6i −7.86883e8 1.81401e9i 9.12044e9 3.13730e10 4.11064e10i
6.19 −1783.43 46763.5i −1.01367e6 2.18366e7i 8.33995e7i 1.78330e9 8.54211e8i 9.28808e9 2.91942e10 3.89441e10i
6.20 −1783.43 46763.5i −1.01367e6 2.18366e7i 8.33995e7i 1.78330e9 + 8.54211e8i 9.28808e9 2.91942e10 3.89441e10i
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 6.60
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 35.23.d.a 60
7.b odd 2 1 inner 35.23.d.a 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.23.d.a 60 1.a even 1 1 trivial
35.23.d.a 60 7.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{23}^{\mathrm{new}}(35, [\chi])\).