Properties

Label 4140.3.d.c
Level $4140$
Weight $3$
Character orbit 4140.d
Analytic conductor $112.807$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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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: no (minimal twist has level 1380)
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
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 24 q^{13} - 64 q^{23} - 160 q^{25} + 60 q^{29} - 4 q^{31} + 60 q^{35} + 108 q^{41} - 136 q^{47} - 428 q^{49} + 120 q^{55} + 84 q^{59} - 188 q^{71} + 472 q^{73} + 120 q^{77} + 60 q^{85} - 80 q^{95}+O(q^{100}) \) 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 11.7218i 0 0 0
2161.2 0 0 0 2.23607i 0 10.9556i 0 0 0
2161.3 0 0 0 2.23607i 0 10.0406i 0 0 0
2161.4 0 0 0 2.23607i 0 4.23458i 0 0 0
2161.5 0 0 0 2.23607i 0 3.01539i 0 0 0
2161.6 0 0 0 2.23607i 0 2.98794i 0 0 0
2161.7 0 0 0 2.23607i 0 2.71701i 0 0 0
2161.8 0 0 0 2.23607i 0 1.24316i 0 0 0
2161.9 0 0 0 2.23607i 0 0.509961i 0 0 0
2161.10 0 0 0 2.23607i 0 2.07606i 0 0 0
2161.11 0 0 0 2.23607i 0 4.95389i 0 0 0
2161.12 0 0 0 2.23607i 0 8.75590i 0 0 0
2161.13 0 0 0 2.23607i 0 9.24833i 0 0 0
2161.14 0 0 0 2.23607i 0 11.3307i 0 0 0
2161.15 0 0 0 2.23607i 0 11.5587i 0 0 0
2161.16 0 0 0 2.23607i 0 11.8989i 0 0 0
2161.17 0 0 0 2.23607i 0 11.8989i 0 0 0
2161.18 0 0 0 2.23607i 0 11.5587i 0 0 0
2161.19 0 0 0 2.23607i 0 11.3307i 0 0 0
2161.20 0 0 0 2.23607i 0 9.24833i 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
23.b odd 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.c 32
3.b odd 2 1 1380.3.d.a 32
23.b odd 2 1 inner 4140.3.d.c 32
69.c even 2 1 1380.3.d.a 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1380.3.d.a 32 3.b odd 2 1
1380.3.d.a 32 69.c even 2 1
4140.3.d.c 32 1.a even 1 1 trivial
4140.3.d.c 32 23.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{32} + 998 T_{7}^{30} + 441911 T_{7}^{28} + 114285060 T_{7}^{26} + 19123041207 T_{7}^{24} + 2167506294182 T_{7}^{22} + 169468469656969 T_{7}^{20} + \cdots + 12\!\cdots\!16 \) acting on \(S_{3}^{\mathrm{new}}(4140, [\chi])\). Copy content Toggle raw display