Properties

Label 4140.3.d.b
Level $4140$
Weight $3$
Character orbit 4140.d
Analytic conductor $112.807$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 4140.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.806829445\)
Analytic rank: \(0\)
Dimension: \(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q - 24 q^{13} - 160 q^{25} - 28 q^{31} - 260 q^{49} + 120 q^{55} - 296 q^{73} - 60 q^{85}+O(q^{100}) \) 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.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2161.1 0 0 0 2.23607i 0 13.2033i 0 0 0
2161.2 0 0 0 2.23607i 0 9.55915i 0 0 0
2161.3 0 0 0 2.23607i 0 8.25712i 0 0 0
2161.4 0 0 0 2.23607i 0 7.68094i 0 0 0
2161.5 0 0 0 2.23607i 0 6.51414i 0 0 0
2161.6 0 0 0 2.23607i 0 4.50512i 0 0 0
2161.7 0 0 0 2.23607i 0 1.15266i 0 0 0
2161.8 0 0 0 2.23607i 0 0.246464i 0 0 0
2161.9 0 0 0 2.23607i 0 0.246464i 0 0 0
2161.10 0 0 0 2.23607i 0 1.15266i 0 0 0
2161.11 0 0 0 2.23607i 0 4.50512i 0 0 0
2161.12 0 0 0 2.23607i 0 6.51414i 0 0 0
2161.13 0 0 0 2.23607i 0 7.68094i 0 0 0
2161.14 0 0 0 2.23607i 0 8.25712i 0 0 0
2161.15 0 0 0 2.23607i 0 9.55915i 0 0 0
2161.16 0 0 0 2.23607i 0 13.2033i 0 0 0
2161.17 0 0 0 2.23607i 0 13.2033i 0 0 0
2161.18 0 0 0 2.23607i 0 9.55915i 0 0 0
2161.19 0 0 0 2.23607i 0 8.25712i 0 0 0
2161.20 0 0 0 2.23607i 0 7.68094i 0 0 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2161.32
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4140.3.d.b 32
3.b odd 2 1 inner 4140.3.d.b 32
23.b odd 2 1 inner 4140.3.d.b 32
69.c even 2 1 inner 4140.3.d.b 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4140.3.d.b 32 1.a even 1 1 trivial
4140.3.d.b 32 3.b odd 2 1 inner
4140.3.d.b 32 23.b odd 2 1 inner
4140.3.d.b 32 69.c even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{16} + 457 T_{7}^{14} + 79883 T_{7}^{12} + 6914455 T_{7}^{10} + 313947096 T_{7}^{8} + 7108236140 T_{7}^{6} + 64495964848 T_{7}^{4} + 77210147648 T_{7}^{2} + 4453693696 \) acting on \(S_{3}^{\mathrm{new}}(4140, [\chi])\). Copy content Toggle raw display