Properties

Label 19.2.e.a
Level $19$
Weight $2$
Character orbit 19.e
Analytic conductor $0.152$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [19,2,Mod(4,19)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(19, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("19.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 19.e (of order \(9\), degree \(6\), 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: \(0.151715763840\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 

Coefficients of the \(q\)-expansion are expressed in terms of a primitive root of unity \(\zeta_{18}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + ( - \zeta_{18}^{2} + \zeta_{18} - 1) q^{2} + ( - \zeta_{18}^{4} + \zeta_{18}^{3} + \zeta_{18}^{2} - 1) q^{3} + (\zeta_{18}^{4} - 2 \zeta_{18}^{3} + \zeta_{18}^{2} - 2 \zeta_{18} + 1) q^{4} + (\zeta_{18}^{5} + \zeta_{18}^{4} - \zeta_{18} - 1) q^{5} + ( - 2 \zeta_{18}^{5} + \zeta_{18}^{4} + \zeta_{18}^{3} - \zeta_{18}) q^{6} + ( - \zeta_{18}^{5} - \zeta_{18}^{4} + \zeta_{18}) q^{7} + (3 \zeta_{18}^{5} - 2 \zeta_{18}^{4} + 2 \zeta_{18}^{3} - 2 \zeta_{18}^{2} + 3 \zeta_{18}) q^{8} + (\zeta_{18}^{4} - 3 \zeta_{18}^{3} + 2 \zeta_{18} + 2) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + ( - \zeta_{18}^{2} + \zeta_{18} - 1) q^{2} + ( - \zeta_{18}^{4} + \zeta_{18}^{3} + \zeta_{18}^{2} - 1) q^{3} + (\zeta_{18}^{4} - 2 \zeta_{18}^{3} + \zeta_{18}^{2} - 2 \zeta_{18} + 1) q^{4} + (\zeta_{18}^{5} + \zeta_{18}^{4} - \zeta_{18} - 1) q^{5} + ( - 2 \zeta_{18}^{5} + \zeta_{18}^{4} + \zeta_{18}^{3} - \zeta_{18}) q^{6} + ( - \zeta_{18}^{5} - \zeta_{18}^{4} + \zeta_{18}) q^{7} + (3 \zeta_{18}^{5} - 2 \zeta_{18}^{4} + 2 \zeta_{18}^{3} - 2 \zeta_{18}^{2} + 3 \zeta_{18}) q^{8} + (\zeta_{18}^{4} - 3 \zeta_{18}^{3} + 2 \zeta_{18} + 2) q^{9} + ( - 2 \zeta_{18}^{4} + \zeta_{18}^{3} + \zeta_{18} + 1) q^{10} + ( - \zeta_{18}^{5} - \zeta_{18}^{4} - \zeta_{18}^{2} - \zeta_{18}) q^{11} + ( - \zeta_{18}^{3} + \zeta_{18}^{2} - \zeta_{18} + 1) q^{12} + (3 \zeta_{18}^{4} + 3 \zeta_{18}^{3} - \zeta_{18} - 2) q^{13} + (2 \zeta_{18}^{4} - \zeta_{18}^{3} + \zeta_{18}^{2} - 2 \zeta_{18}) q^{14} + (\zeta_{18}^{4} - \zeta_{18}^{3} - \zeta_{18}^{2} - \zeta_{18} + 1) q^{15} + ( - 3 \zeta_{18}^{5} + \zeta_{18}^{4} + 3 \zeta_{18}^{2} - 3) q^{16} + (\zeta_{18}^{5} - \zeta_{18}^{3} - 2 \zeta_{18} + 1) q^{17} + (4 \zeta_{18}^{5} - 4 \zeta_{18}^{4} - 1) q^{18} + (\zeta_{18}^{5} - 4 \zeta_{18}^{4} - 2 \zeta_{18}^{2} + 2 \zeta_{18} - 2) q^{19} + ( - 3 \zeta_{18}^{5} + \zeta_{18}^{4} + 2 \zeta_{18}^{2} + 2 \zeta_{18} - 1) q^{20} + \zeta_{18} q^{21} + 3 \zeta_{18}^{4} q^{22} + (2 \zeta_{18}^{3} - 2 \zeta_{18}^{2} + 2 \zeta_{18}) q^{23} + ( - \zeta_{18}^{5} + 2 \zeta_{18}^{4} + 3 \zeta_{18}^{3} - 3 \zeta_{18}^{2} - 2 \zeta_{18} + 1) q^{24} + (2 \zeta_{18}^{5} - 2 \zeta_{18}^{4} - 2 \zeta_{18}^{3} + \zeta_{18} + 1) q^{25} + ( - 5 \zeta_{18}^{3} + \zeta_{18}^{2} - \zeta_{18} + 5) q^{26} + ( - 3 \zeta_{18}^{5} + 3 \zeta_{18}^{4} + 2 \zeta_{18}^{3} + 3 \zeta_{18}^{2} - 3 \zeta_{18}) q^{27} + (3 \zeta_{18}^{5} - 2 \zeta_{18}^{4} + 2 \zeta_{18}^{3} - 3 \zeta_{18}^{2}) q^{28} + ( - 5 \zeta_{18}^{5} + \zeta_{18}^{3} + 5 \zeta_{18}^{2} - \zeta_{18} - 1) q^{29} + (2 \zeta_{18}^{5} - \zeta_{18}^{4} - \zeta_{18}^{2} + 2 \zeta_{18}) q^{30} + (3 \zeta_{18}^{5} + 3 \zeta_{18}^{4} - 3 \zeta_{18}^{3} - 2 \zeta_{18}^{2} - \zeta_{18} + 3) q^{31} + ( - 3 \zeta_{18}^{4} - 3 \zeta_{18}^{3} + 3) q^{32} + (\zeta_{18}^{5} - 3 \zeta_{18}^{4} - \zeta_{18}^{3} + \zeta_{18}^{2} + 3 \zeta_{18} - 1) q^{33} + ( - 2 \zeta_{18}^{4} + 4 \zeta_{18}^{3} - 3 \zeta_{18}^{2} + 4 \zeta_{18} - 2) q^{34} + (2 \zeta_{18}^{5} + \zeta_{18}^{4} + 2 \zeta_{18}^{3}) q^{35} + ( - 2 \zeta_{18}^{5} + 2 \zeta_{18}^{3} - 3 \zeta_{18}^{2} + 3 \zeta_{18} - 5) q^{36} + ( - 2 \zeta_{18}^{5} + 3 \zeta_{18}^{4} - \zeta_{18}^{2} - \zeta_{18}) q^{37} + ( - 5 \zeta_{18}^{5} + 5 \zeta_{18}^{4} + \zeta_{18}^{3} + 6 \zeta_{18}^{2} - 3 \zeta_{18} - 3) q^{38} + (\zeta_{18}^{5} - 2 \zeta_{18}^{4} + \zeta_{18}^{2} + \zeta_{18} - 4) q^{39} + (2 \zeta_{18}^{5} - 2 \zeta_{18}^{3} - \zeta_{18}^{2} - 6 \zeta_{18} + 1) q^{40} + (3 \zeta_{18}^{5} - 4 \zeta_{18}^{4} - \zeta_{18}^{3} - 4 \zeta_{18}^{2} + 4) q^{41} + ( - \zeta_{18}^{3} + \zeta_{18}^{2} - \zeta_{18}) q^{42} + ( - 2 \zeta_{18}^{5} - 5 \zeta_{18}^{3} + 5 \zeta_{18}^{2} + 2) q^{43} + (3 \zeta_{18}^{5} + \zeta_{18}^{4} + \zeta_{18}^{3} - 2 \zeta_{18} + 1) q^{44} + (\zeta_{18}^{5} + \zeta_{18}^{4} + 5 \zeta_{18}^{3} - \zeta_{18} - 5) q^{45} + ( - 2 \zeta_{18}^{5} + 4 \zeta_{18}^{4} - 6 \zeta_{18}^{3} + 4 \zeta_{18}^{2} - 2 \zeta_{18}) q^{46} + ( - 2 \zeta_{18}^{5} - \zeta_{18}^{4} + 3 \zeta_{18}^{3} + 2 \zeta_{18}^{2} - 2 \zeta_{18} - 2) q^{47} + (2 \zeta_{18}^{5} + 3 \zeta_{18}^{4} - 5 \zeta_{18}^{3} - 2 \zeta_{18}^{2} + 2 \zeta_{18} + 2) q^{48} + ( - \zeta_{18}^{5} + 5 \zeta_{18}^{3} - \zeta_{18}) q^{49} + ( - 2 \zeta_{18}^{5} - 2 \zeta_{18}^{4} + 5 \zeta_{18}^{3} + 2 \zeta_{18} - 5) q^{50} + (\zeta_{18}^{5} - \zeta_{18}^{4} - \zeta_{18}^{3} + 1) q^{51} + ( - \zeta_{18}^{5} - 6 \zeta_{18}^{4} + 3 \zeta_{18}^{3} - 3 \zeta_{18}^{2} + 6 \zeta_{18} + 1) q^{52} + (\zeta_{18}^{4} - 3 \zeta_{18}^{3} - 2 \zeta_{18}^{2} - 3 \zeta_{18} + 1) q^{53} + (4 \zeta_{18}^{5} - \zeta_{18}^{4} - 2 \zeta_{18}^{3} - 6 \zeta_{18}^{2} + 6) q^{54} + (3 \zeta_{18}^{2} + 3 \zeta_{18} + 3) q^{55} + ( - 5 \zeta_{18}^{5} + 2 \zeta_{18}^{4} + 3 \zeta_{18}^{2} + 3 \zeta_{18} - 1) q^{56} + (3 \zeta_{18}^{4} - 2 \zeta_{18}^{3} - 5 \zeta_{18}^{2} + \zeta_{18} + 5) q^{57} + (4 \zeta_{18}^{5} + \zeta_{18}^{4} - 5 \zeta_{18}^{2} - 5 \zeta_{18} + 6) q^{58} + (2 \zeta_{18}^{2} + 7 \zeta_{18} + 2) q^{59} + ( - \zeta_{18}^{5} + 2 \zeta_{18}^{4} + \zeta_{18}^{2} - 1) q^{60} + ( - 4 \zeta_{18}^{4} + 4 \zeta_{18}^{3} + 3 \zeta_{18}^{2} + 4 \zeta_{18} - 4) q^{61} + (3 \zeta_{18}^{5} - 7 \zeta_{18}^{4} + 2 \zeta_{18}^{3} - 2 \zeta_{18}^{2} + 7 \zeta_{18} - 3) q^{62} + ( - \zeta_{18}^{5} - 2 \zeta_{18}^{4} - 2 \zeta_{18}^{3} - \zeta_{18} + 3) q^{63} + (4 \zeta_{18}^{3} + 3 \zeta_{18}^{2} - 3 \zeta_{18} - 4) q^{64} + ( - 5 \zeta_{18}^{4} - 4 \zeta_{18}^{3} - 5 \zeta_{18}^{2}) q^{65} + ( - 3 \zeta_{18}^{5} + 3 \zeta_{18}^{3} + 3 \zeta_{18}^{2} - 3 \zeta_{18} - 3) q^{66} + (6 \zeta_{18}^{5} + 6 \zeta_{18}^{4} - 2 \zeta_{18}^{3} - 6 \zeta_{18}^{2} - 4 \zeta_{18} - 4) q^{67} + ( - 4 \zeta_{18}^{5} + 7 \zeta_{18}^{4} - 5 \zeta_{18}^{3} + 7 \zeta_{18}^{2} - 4 \zeta_{18}) q^{68} + ( - 2 \zeta_{18}^{5} - 2 \zeta_{18}^{4} + 4 \zeta_{18}^{3} + 2 \zeta_{18}^{2} - 4) q^{69} + ( - 3 \zeta_{18}^{5} - \zeta_{18}^{4} - \zeta_{18}^{3} + 2 \zeta_{18} - 1) q^{70} + (2 \zeta_{18}^{5} + 10 \zeta_{18}^{4} + 2 \zeta_{18}^{3} - 2 \zeta_{18}^{2} - 10 \zeta_{18} - 2) q^{71} + ( - \zeta_{18}^{4} - 2 \zeta_{18}^{3} + 13 \zeta_{18}^{2} - 2 \zeta_{18} - 1) q^{72} + ( - 4 \zeta_{18}^{5} - 4 \zeta_{18}^{3}) q^{73} + (5 \zeta_{18}^{5} - 5 \zeta_{18}^{3} - \zeta_{18} + 5) q^{74} + ( - \zeta_{18}^{5} + 4 \zeta_{18}^{4} - 3 \zeta_{18}^{2} - 3 \zeta_{18} + 5) q^{75} + (9 \zeta_{18}^{5} - 3 \zeta_{18}^{4} + 2 \zeta_{18}^{3} - 2 \zeta_{18}^{2} - 3 \zeta_{18} + 5) q^{76} + (\zeta_{18}^{5} + \zeta_{18}^{4} - 2 \zeta_{18}^{2} - 2 \zeta_{18} - 3) q^{77} + ( - 3 \zeta_{18}^{5} + 3 \zeta_{18}^{3} + 4 \zeta_{18}^{2} - 4 \zeta_{18} + 1) q^{78} + ( - 7 \zeta_{18}^{5} - 3 \zeta_{18}^{4} - \zeta_{18}^{3} + 6 \zeta_{18}^{2} - 6) q^{79} + ( - \zeta_{18}^{4} + 3 \zeta_{18}^{3} - 4 \zeta_{18}^{2} + 3 \zeta_{18} - 1) q^{80} + ( - \zeta_{18}^{5} - 5 \zeta_{18}^{4} + 5 \zeta_{18} + 1) q^{81} + ( - 6 \zeta_{18}^{5} + 4 \zeta_{18}^{4} + 4 \zeta_{18}^{3} + 7 \zeta_{18} - 11) q^{82} + (3 \zeta_{18}^{5} + 3 \zeta_{18}^{4} - 9 \zeta_{18}^{2} + 6 \zeta_{18}) q^{83} + (\zeta_{18}^{5} - 2 \zeta_{18}^{4} + \zeta_{18}^{3} - 2 \zeta_{18}^{2} + \zeta_{18}) q^{84} + ( - 3 \zeta_{18}^{5} + \zeta_{18}^{4} - 2 \zeta_{18}^{3} + 3 \zeta_{18}^{2} + \zeta_{18} + 1) q^{85} + (7 \zeta_{18}^{5} - 8 \zeta_{18}^{4} + 8 \zeta_{18}^{3} - 7 \zeta_{18}^{2}) q^{86} + (7 \zeta_{18}^{5} - \zeta_{18}^{4} - 7 \zeta_{18}^{3} - \zeta_{18}^{2} + 7 \zeta_{18}) q^{87} + ( - 3 \zeta_{18}^{5} - 3 \zeta_{18}^{4} - 3 \zeta_{18}^{3} - 3 \zeta_{18}^{2} + 6 \zeta_{18} + 3) q^{88} + (5 \zeta_{18}^{5} - 2 \zeta_{18}^{4} - 2 \zeta_{18}^{3} + 3 \zeta_{18} - 1) q^{89} + ( - 5 \zeta_{18}^{5} + 3 \zeta_{18}^{4} - 4 \zeta_{18}^{3} + 4 \zeta_{18}^{2} - 3 \zeta_{18} + 5) q^{90} + (2 \zeta_{18}^{4} + \zeta_{18}^{3} + 5 \zeta_{18}^{2} + \zeta_{18} + 2) q^{91} + (8 \zeta_{18}^{5} - 8 \zeta_{18}^{4} + 2 \zeta_{18}^{3} - 6 \zeta_{18}^{2} + 6) q^{92} + ( - 7 \zeta_{18}^{5} + 7 \zeta_{18}^{3} + 5 \zeta_{18}^{2} - 8 \zeta_{18} - 2) q^{93} + ( - 2 \zeta_{18}^{5} + 4 \zeta_{18}^{4} - 2 \zeta_{18}^{2} - 2 \zeta_{18} + 3) q^{94} + ( - \zeta_{18}^{5} + \zeta_{18}^{3} + 4 \zeta_{18}^{2} + \zeta_{18} + 6) q^{95} + 3 q^{96} + ( - 2 \zeta_{18}^{5} + 2 \zeta_{18}^{3} + 4 \zeta_{18}^{2} - 5 \zeta_{18} + 2) q^{97} + ( - 4 \zeta_{18}^{5} + 6 \zeta_{18}^{4} - 5 \zeta_{18}^{3} - \zeta_{18}^{2} + 1) q^{98} + (4 \zeta_{18}^{4} - 5 \zeta_{18}^{3} - 6 \zeta_{18}^{2} - 5 \zeta_{18} + 4) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9} + 9 q^{10} + 3 q^{12} - 3 q^{13} - 3 q^{14} + 3 q^{15} - 18 q^{16} + 3 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} + 6 q^{23} + 15 q^{24} + 15 q^{26} + 6 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 9 q^{33} + 6 q^{35} - 24 q^{36} - 15 q^{38} - 24 q^{39} + 21 q^{41} - 3 q^{42} - 3 q^{43} + 9 q^{44} - 15 q^{45} - 18 q^{46} - 3 q^{47} - 3 q^{48} + 15 q^{49} - 15 q^{50} + 3 q^{51} + 15 q^{52} - 3 q^{53} + 30 q^{54} + 18 q^{55} - 6 q^{56} + 24 q^{57} + 36 q^{58} + 12 q^{59} - 6 q^{60} - 12 q^{61} - 12 q^{62} + 12 q^{63} - 12 q^{64} - 12 q^{65} - 9 q^{66} - 30 q^{67} - 15 q^{68} - 12 q^{69} - 9 q^{70} - 6 q^{71} - 12 q^{72} - 12 q^{73} + 15 q^{74} + 30 q^{75} + 36 q^{76} - 18 q^{77} + 15 q^{78} - 39 q^{79} + 3 q^{80} + 6 q^{81} - 54 q^{82} + 3 q^{84} + 24 q^{86} - 21 q^{87} + 9 q^{88} - 12 q^{89} + 18 q^{90} + 15 q^{91} + 42 q^{92} + 9 q^{93} + 18 q^{94} + 39 q^{95} + 18 q^{96} + 18 q^{97} - 9 q^{98} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(\zeta_{18}^{2}\)

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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4.1
0.939693 + 0.342020i
0.939693 0.342020i
−0.766044 + 0.642788i
−0.173648 0.984808i
−0.766044 0.642788i
−0.173648 + 0.984808i
−0.826352 0.300767i 0.0923963 + 0.524005i −0.939693 0.788496i −1.93969 + 1.62760i 0.0812519 0.460802i 0.939693 1.62760i 1.41875 + 2.45734i 2.55303 0.929228i 2.09240 0.761570i
5.1 −0.826352 + 0.300767i 0.0923963 0.524005i −0.939693 + 0.788496i −1.93969 1.62760i 0.0812519 + 0.460802i 0.939693 + 1.62760i 1.41875 2.45734i 2.55303 + 0.929228i 2.09240 + 0.761570i
6.1 −1.93969 + 1.62760i 0.613341 + 0.223238i 0.766044 4.34445i −0.233956 1.32683i −1.55303 + 0.565258i −0.766044 + 1.32683i 3.05303 + 5.28801i −1.97178 1.65452i 2.61334 + 2.19285i
9.1 −0.233956 1.32683i −2.20574 + 1.85083i 0.173648 0.0632028i −0.826352 0.300767i 2.97178 + 2.49362i −0.173648 + 0.300767i −1.47178 2.54920i 0.918748 5.21048i −0.205737 + 1.16679i
16.1 −1.93969 1.62760i 0.613341 0.223238i 0.766044 + 4.34445i −0.233956 + 1.32683i −1.55303 0.565258i −0.766044 1.32683i 3.05303 5.28801i −1.97178 + 1.65452i 2.61334 2.19285i
17.1 −0.233956 + 1.32683i −2.20574 1.85083i 0.173648 + 0.0632028i −0.826352 + 0.300767i 2.97178 2.49362i −0.173648 0.300767i −1.47178 + 2.54920i 0.918748 + 5.21048i −0.205737 1.16679i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 4.1
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.e even 9 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 19.2.e.a 6
3.b odd 2 1 171.2.u.c 6
4.b odd 2 1 304.2.u.b 6
5.b even 2 1 475.2.l.a 6
5.c odd 4 2 475.2.u.a 12
7.b odd 2 1 931.2.w.a 6
7.c even 3 1 931.2.v.b 6
7.c even 3 1 931.2.x.a 6
7.d odd 6 1 931.2.v.a 6
7.d odd 6 1 931.2.x.b 6
19.b odd 2 1 361.2.e.h 6
19.c even 3 1 361.2.e.f 6
19.c even 3 1 361.2.e.g 6
19.d odd 6 1 361.2.e.a 6
19.d odd 6 1 361.2.e.b 6
19.e even 9 1 inner 19.2.e.a 6
19.e even 9 1 361.2.a.g 3
19.e even 9 2 361.2.c.i 6
19.e even 9 1 361.2.e.f 6
19.e even 9 1 361.2.e.g 6
19.f odd 18 1 361.2.a.h 3
19.f odd 18 2 361.2.c.h 6
19.f odd 18 1 361.2.e.a 6
19.f odd 18 1 361.2.e.b 6
19.f odd 18 1 361.2.e.h 6
57.j even 18 1 3249.2.a.s 3
57.l odd 18 1 171.2.u.c 6
57.l odd 18 1 3249.2.a.z 3
76.k even 18 1 5776.2.a.bi 3
76.l odd 18 1 304.2.u.b 6
76.l odd 18 1 5776.2.a.br 3
95.o odd 18 1 9025.2.a.x 3
95.p even 18 1 475.2.l.a 6
95.p even 18 1 9025.2.a.bd 3
95.q odd 36 2 475.2.u.a 12
133.u even 9 1 931.2.x.a 6
133.w even 9 1 931.2.v.b 6
133.x odd 18 1 931.2.x.b 6
133.y odd 18 1 931.2.w.a 6
133.z odd 18 1 931.2.v.a 6
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
19.2.e.a 6 1.a even 1 1 trivial
19.2.e.a 6 19.e even 9 1 inner
171.2.u.c 6 3.b odd 2 1
171.2.u.c 6 57.l odd 18 1
304.2.u.b 6 4.b odd 2 1
304.2.u.b 6 76.l odd 18 1
361.2.a.g 3 19.e even 9 1
361.2.a.h 3 19.f odd 18 1
361.2.c.h 6 19.f odd 18 2
361.2.c.i 6 19.e even 9 2
361.2.e.a 6 19.d odd 6 1
361.2.e.a 6 19.f odd 18 1
361.2.e.b 6 19.d odd 6 1
361.2.e.b 6 19.f odd 18 1
361.2.e.f 6 19.c even 3 1
361.2.e.f 6 19.e even 9 1
361.2.e.g 6 19.c even 3 1
361.2.e.g 6 19.e even 9 1
361.2.e.h 6 19.b odd 2 1
361.2.e.h 6 19.f odd 18 1
475.2.l.a 6 5.b even 2 1
475.2.l.a 6 95.p even 18 1
475.2.u.a 12 5.c odd 4 2
475.2.u.a 12 95.q odd 36 2
931.2.v.a 6 7.d odd 6 1
931.2.v.a 6 133.z odd 18 1
931.2.v.b 6 7.c even 3 1
931.2.v.b 6 133.w even 9 1
931.2.w.a 6 7.b odd 2 1
931.2.w.a 6 133.y odd 18 1
931.2.x.a 6 7.c even 3 1
931.2.x.a 6 133.u even 9 1
931.2.x.b 6 7.d odd 6 1
931.2.x.b 6 133.x odd 18 1
3249.2.a.s 3 57.j even 18 1
3249.2.a.z 3 57.l odd 18 1
5776.2.a.bi 3 76.k even 18 1
5776.2.a.br 3 76.l odd 18 1
9025.2.a.x 3 95.o odd 18 1
9025.2.a.bd 3 95.p even 18 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(19, [\chi])\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{6} + 6 T^{5} + 18 T^{4} + 30 T^{3} + \cdots + 9 \) Copy content Toggle raw display
$3$ \( T^{6} + 3 T^{5} + 3 T^{4} - 8 T^{3} + \cdots + 1 \) Copy content Toggle raw display
$5$ \( T^{6} + 6 T^{5} + 18 T^{4} + 30 T^{3} + \cdots + 9 \) Copy content Toggle raw display
$7$ \( T^{6} + 3 T^{4} + 2 T^{3} + 9 T^{2} + \cdots + 1 \) Copy content Toggle raw display
$11$ \( T^{6} + 9 T^{4} - 18 T^{3} + 81 T^{2} + \cdots + 81 \) Copy content Toggle raw display
$13$ \( T^{6} + 3 T^{5} + 24 T^{4} + \cdots + 1369 \) Copy content Toggle raw display
$17$ \( T^{6} - 3 T^{5} + 30 T^{3} + 36 T^{2} + \cdots + 9 \) Copy content Toggle raw display
$19$ \( T^{6} + 12 T^{5} + 78 T^{4} + \cdots + 6859 \) Copy content Toggle raw display
$23$ \( T^{6} - 6 T^{5} + 36 T^{4} - 192 T^{3} + \cdots + 576 \) Copy content Toggle raw display
$29$ \( T^{6} + 3 T^{5} + 36 T^{4} + \cdots + 12321 \) Copy content Toggle raw display
$31$ \( T^{6} - 9 T^{5} + 75 T^{4} + \cdots + 2809 \) Copy content Toggle raw display
$37$ \( (T^{3} - 21 T - 17)^{2} \) Copy content Toggle raw display
$41$ \( T^{6} - 21 T^{5} + 162 T^{4} + \cdots + 12321 \) Copy content Toggle raw display
$43$ \( T^{6} + 3 T^{5} + 60 T^{4} + \cdots + 26569 \) Copy content Toggle raw display
$47$ \( T^{6} + 3 T^{5} + 54 T^{4} + 24 T^{3} + \cdots + 9 \) Copy content Toggle raw display
$53$ \( T^{6} + 3 T^{5} - 84 T^{3} + \cdots + 2601 \) Copy content Toggle raw display
$59$ \( T^{6} - 12 T^{5} + 18 T^{4} + \cdots + 71289 \) Copy content Toggle raw display
$61$ \( T^{6} + 12 T^{5} + 24 T^{4} + \cdots + 32761 \) Copy content Toggle raw display
$67$ \( T^{6} + 30 T^{5} + 348 T^{4} + \cdots + 179776 \) Copy content Toggle raw display
$71$ \( T^{6} + 6 T^{5} - 36 T^{4} + \cdots + 788544 \) Copy content Toggle raw display
$73$ \( T^{6} + 12 T^{5} + 96 T^{4} + \cdots + 4096 \) Copy content Toggle raw display
$79$ \( T^{6} + 39 T^{5} + 708 T^{4} + \cdots + 654481 \) Copy content Toggle raw display
$83$ \( T^{6} + 189 T^{4} + 918 T^{3} + \cdots + 210681 \) Copy content Toggle raw display
$89$ \( T^{6} + 12 T^{5} + 54 T^{4} + \cdots + 3249 \) Copy content Toggle raw display
$97$ \( T^{6} - 18 T^{5} + 234 T^{4} + \cdots + 16129 \) Copy content Toggle raw display
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