Properties

Label 4140.2.n.b
Level $4140$
Weight $2$
Character orbit 4140.n
Analytic conductor $33.058$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(33.0580664368\)
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
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 56 q^{25} + 16 q^{31} - 96 q^{49} - 16 q^{55} - 40 q^{85}+O(q^{100}) \) 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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2069.1 0 0 0 −2.23315 0.114288i 0 −3.07318 0 0 0
2069.2 0 0 0 −2.23315 0.114288i 0 3.07318 0 0 0
2069.3 0 0 0 −2.23315 + 0.114288i 0 −3.07318 0 0 0
2069.4 0 0 0 −2.23315 + 0.114288i 0 3.07318 0 0 0
2069.5 0 0 0 −1.83744 1.27428i 0 −0.920125 0 0 0
2069.6 0 0 0 −1.83744 1.27428i 0 0.920125 0 0 0
2069.7 0 0 0 −1.83744 + 1.27428i 0 −0.920125 0 0 0
2069.8 0 0 0 −1.83744 + 1.27428i 0 0.920125 0 0 0
2069.9 0 0 0 −1.64510 1.51448i 0 −2.05693 0 0 0
2069.10 0 0 0 −1.64510 1.51448i 0 2.05693 0 0 0
2069.11 0 0 0 −1.64510 + 1.51448i 0 −2.05693 0 0 0
2069.12 0 0 0 −1.64510 + 1.51448i 0 2.05693 0 0 0
2069.13 0 0 0 −1.55901 1.60296i 0 −1.21571 0 0 0
2069.14 0 0 0 −1.55901 1.60296i 0 1.21571 0 0 0
2069.15 0 0 0 −1.55901 + 1.60296i 0 −1.21571 0 0 0
2069.16 0 0 0 −1.55901 + 1.60296i 0 1.21571 0 0 0
2069.17 0 0 0 1.55901 1.60296i 0 −1.21571 0 0 0
2069.18 0 0 0 1.55901 1.60296i 0 1.21571 0 0 0
2069.19 0 0 0 1.55901 + 1.60296i 0 −1.21571 0 0 0
2069.20 0 0 0 1.55901 + 1.60296i 0 1.21571 0 0 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2069.32
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
15.d odd 2 1 inner
23.b odd 2 1 inner
69.c even 2 1 inner
115.c odd 2 1 inner
345.h even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4140.2.n.b 32
3.b odd 2 1 inner 4140.2.n.b 32
5.b even 2 1 inner 4140.2.n.b 32
15.d odd 2 1 inner 4140.2.n.b 32
23.b odd 2 1 inner 4140.2.n.b 32
69.c even 2 1 inner 4140.2.n.b 32
115.c odd 2 1 inner 4140.2.n.b 32
345.h even 2 1 inner 4140.2.n.b 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4140.2.n.b 32 1.a even 1 1 trivial
4140.2.n.b 32 3.b odd 2 1 inner
4140.2.n.b 32 5.b even 2 1 inner
4140.2.n.b 32 15.d odd 2 1 inner
4140.2.n.b 32 23.b odd 2 1 inner
4140.2.n.b 32 69.c even 2 1 inner
4140.2.n.b 32 115.c odd 2 1 inner
4140.2.n.b 32 345.h even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{8} - 16T_{7}^{6} + 73T_{7}^{4} - 110T_{7}^{2} + 50 \) acting on \(S_{2}^{\mathrm{new}}(4140, [\chi])\). Copy content Toggle raw display