Properties

Label 2916.3.c.b
Level 2916
Weight 3
Character orbit 2916.c
Analytic conductor 79.455
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 2916 = 2^{2} \cdot 3^{6} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2916.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(79.4552450875\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: no (minimal twist has level 108)
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.

\(\operatorname{Tr}(f)(q) = \) \( 36q + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 36q - 180q^{25} + 252q^{49} + 18q^{61} - 90q^{67} + 126q^{73} - 198q^{91} + O(q^{100}) \)

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.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1457.1 0 0 0 9.50324i 0 2.36132 0 0 0
1457.2 0 0 0 8.78835i 0 −4.31308 0 0 0
1457.3 0 0 0 7.78294i 0 3.61169 0 0 0
1457.4 0 0 0 7.77099i 0 13.6742 0 0 0
1457.5 0 0 0 7.31297i 0 −9.37121 0 0 0
1457.6 0 0 0 7.21405i 0 −4.39191 0 0 0
1457.7 0 0 0 5.21679i 0 −11.6618 0 0 0
1457.8 0 0 0 4.83775i 0 9.71048 0 0 0
1457.9 0 0 0 4.39539i 0 −3.57384 0 0 0
1457.10 0 0 0 4.19339i 0 −11.8514 0 0 0
1457.11 0 0 0 4.17955i 0 5.19980 0 0 0
1457.12 0 0 0 3.70301i 0 −0.419343 0 0 0
1457.13 0 0 0 3.34301i 0 5.01893 0 0 0
1457.14 0 0 0 2.96937i 0 0.934448 0 0 0
1457.15 0 0 0 2.16582i 0 6.23376 0 0 0
1457.16 0 0 0 1.52502i 0 −3.44709 0 0 0
1457.17 0 0 0 0.464464i 0 10.8001 0 0 0
1457.18 0 0 0 0.200781i 0 −8.51501 0 0 0
1457.19 0 0 0 0.200781i 0 −8.51501 0 0 0
1457.20 0 0 0 0.464464i 0 10.8001 0 0 0
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1457.36
Significant digits:
Format:

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 2916.3.c.b 36
3.b odd 2 1 inner 2916.3.c.b 36
27.e even 9 1 108.3.k.a 36
27.e even 9 1 324.3.k.a 36
27.f odd 18 1 108.3.k.a 36
27.f odd 18 1 324.3.k.a 36
108.j odd 18 1 432.3.bc.b 36
108.l even 18 1 432.3.bc.b 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
108.3.k.a 36 27.e even 9 1
108.3.k.a 36 27.f odd 18 1
324.3.k.a 36 27.e even 9 1
324.3.k.a 36 27.f odd 18 1
432.3.bc.b 36 108.j odd 18 1
432.3.bc.b 36 108.l even 18 1
2916.3.c.b 36 1.a even 1 1 trivial
2916.3.c.b 36 3.b odd 2 1 inner

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database