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Properties

Label 7803.2.a.cf
Level $7803$
Weight $2$
Character orbit 7803.a
Self dual yes
Analytic conductor $62.307$
Analytic rank $0$
Dimension $24$
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] = [7803,2,Mod(1,7803)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7803, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7803.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7803 = 3^{3} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7803.a (trivial)

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: yes
Analytic conductor: \(62.3072686972\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 459)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{4} + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{4} + 16 q^{7} + 16 q^{10} - 8 q^{13} + 24 q^{16} - 8 q^{19} + 56 q^{22} + 16 q^{25} + 16 q^{31} + 72 q^{37} + 72 q^{40} - 8 q^{43} + 40 q^{46} + 24 q^{49} - 32 q^{52} - 40 q^{55} + 72 q^{58} + 48 q^{61} + 48 q^{64} - 32 q^{67} + 24 q^{70} + 88 q^{73} + 8 q^{76} + 8 q^{82} + 144 q^{88} + 56 q^{91} + 72 q^{94} + 112 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.78932 0 5.78032 −2.20458 0 0.760317 −10.5445 0 6.14928
1.2 −2.46855 0 4.09372 −0.386744 0 −0.376057 −5.16844 0 0.954695
1.3 −2.38752 0 3.70025 −3.70246 0 0.490173 −4.05937 0 8.83969
1.4 −2.11654 0 2.47974 2.00938 0 3.83191 −1.01538 0 −4.25294
1.5 −1.80499 0 1.25799 2.72926 0 −3.09089 1.33933 0 −4.92629
1.6 −1.73279 0 1.00255 −0.674959 0 −3.57979 1.72836 0 1.16956
1.7 −1.61878 0 0.620447 0.812904 0 2.09960 2.23319 0 −1.31591
1.8 −1.20664 0 −0.544018 1.31073 0 4.60071 3.06972 0 −1.58158
1.9 −0.934034 0 −1.12758 0.862367 0 −2.40335 2.92127 0 −0.805480
1.10 −0.787178 0 −1.38035 −3.87422 0 4.77940 2.66094 0 3.04970
1.11 −0.321706 0 −1.89651 −3.28262 0 1.74788 1.25353 0 1.05604
1.12 −0.115970 0 −1.98655 2.90385 0 −0.859917 0.462322 0 −0.336760
1.13 0.115970 0 −1.98655 −2.90385 0 −0.859917 −0.462322 0 −0.336760
1.14 0.321706 0 −1.89651 3.28262 0 1.74788 −1.25353 0 1.05604
1.15 0.787178 0 −1.38035 3.87422 0 4.77940 −2.66094 0 3.04970
1.16 0.934034 0 −1.12758 −0.862367 0 −2.40335 −2.92127 0 −0.805480
1.17 1.20664 0 −0.544018 −1.31073 0 4.60071 −3.06972 0 −1.58158
1.18 1.61878 0 0.620447 −0.812904 0 2.09960 −2.23319 0 −1.31591
1.19 1.73279 0 1.00255 0.674959 0 −3.57979 −1.72836 0 1.16956
1.20 1.80499 0 1.25799 −2.72926 0 −3.09089 −1.33933 0 −4.92629
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(17\) \(-1\)

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 7803.2.a.cf 24
3.b odd 2 1 inner 7803.2.a.cf 24
17.b even 2 1 7803.2.a.ce 24
17.e odd 16 2 459.2.l.b ✓ 48
51.c odd 2 1 7803.2.a.ce 24
51.i even 16 2 459.2.l.b ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
459.2.l.b ✓ 48 17.e odd 16 2
459.2.l.b ✓ 48 51.i even 16 2
7803.2.a.ce 24 17.b even 2 1
7803.2.a.ce 24 51.c odd 2 1
7803.2.a.cf 24 1.a even 1 1 trivial
7803.2.a.cf 24 3.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7803))\):

\( T_{2}^{24} - 36 T_{2}^{22} + 558 T_{2}^{20} - 4888 T_{2}^{18} + 26699 T_{2}^{16} - 94624 T_{2}^{14} + \cdots + 34 \) Copy content Toggle raw display
\( T_{5}^{24} - 68 T_{5}^{22} + 1962 T_{5}^{20} - 31408 T_{5}^{18} + 306393 T_{5}^{16} - 1885408 T_{5}^{14} + \cdots + 157216 \) Copy content Toggle raw display
\( T_{7}^{12} - 8 T_{7}^{11} - 16 T_{7}^{10} + 236 T_{7}^{9} - 88 T_{7}^{8} - 2280 T_{7}^{7} + 2406 T_{7}^{6} + \cdots - 991 \) Copy content Toggle raw display
\( T_{11}^{24} - 168 T_{11}^{22} + 12164 T_{11}^{20} - 497704 T_{11}^{18} + 12691532 T_{11}^{16} + \cdots + 11954400034 \) Copy content Toggle raw display