Properties

Label 1152.3.j.a
Level $1152$
Weight $3$
Character orbit 1152.j
Analytic conductor $31.390$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1152.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(31.3897264543\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32q + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 32q - 64q^{19} - 128q^{43} - 224q^{49} - 64q^{61} + 64q^{67} - 512q^{79} - 320q^{85} + 192q^{91} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
161.1 0 0 0 −6.08688 6.08688i 0 9.40026i 0 0 0
161.2 0 0 0 −5.52702 5.52702i 0 7.79421i 0 0 0
161.3 0 0 0 −5.14405 5.14405i 0 7.48880i 0 0 0
161.4 0 0 0 −3.90343 3.90343i 0 0.778757i 0 0 0
161.5 0 0 0 −1.92848 1.92848i 0 2.43162i 0 0 0
161.6 0 0 0 −1.84570 1.84570i 0 0.226665i 0 0 0
161.7 0 0 0 −1.66372 1.66372i 0 13.3224i 0 0 0
161.8 0 0 0 −0.900179 0.900179i 0 7.66460i 0 0 0
161.9 0 0 0 0.900179 + 0.900179i 0 7.66460i 0 0 0
161.10 0 0 0 1.66372 + 1.66372i 0 13.3224i 0 0 0
161.11 0 0 0 1.84570 + 1.84570i 0 0.226665i 0 0 0
161.12 0 0 0 1.92848 + 1.92848i 0 2.43162i 0 0 0
161.13 0 0 0 3.90343 + 3.90343i 0 0.778757i 0 0 0
161.14 0 0 0 5.14405 + 5.14405i 0 7.48880i 0 0 0
161.15 0 0 0 5.52702 + 5.52702i 0 7.79421i 0 0 0
161.16 0 0 0 6.08688 + 6.08688i 0 9.40026i 0 0 0
737.1 0 0 0 −6.08688 + 6.08688i 0 9.40026i 0 0 0
737.2 0 0 0 −5.52702 + 5.52702i 0 7.79421i 0 0 0
737.3 0 0 0 −5.14405 + 5.14405i 0 7.48880i 0 0 0
737.4 0 0 0 −3.90343 + 3.90343i 0 0.778757i 0 0 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 737.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
16.e even 4 1 inner
48.i odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1152.3.j.a 32
3.b odd 2 1 inner 1152.3.j.a 32
4.b odd 2 1 1152.3.j.b 32
8.b even 2 1 144.3.j.a 32
8.d odd 2 1 576.3.j.a 32
12.b even 2 1 1152.3.j.b 32
16.e even 4 1 144.3.j.a 32
16.e even 4 1 inner 1152.3.j.a 32
16.f odd 4 1 576.3.j.a 32
16.f odd 4 1 1152.3.j.b 32
24.f even 2 1 576.3.j.a 32
24.h odd 2 1 144.3.j.a 32
48.i odd 4 1 144.3.j.a 32
48.i odd 4 1 inner 1152.3.j.a 32
48.k even 4 1 576.3.j.a 32
48.k even 4 1 1152.3.j.b 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
144.3.j.a 32 8.b even 2 1
144.3.j.a 32 16.e even 4 1
144.3.j.a 32 24.h odd 2 1
144.3.j.a 32 48.i odd 4 1
576.3.j.a 32 8.d odd 2 1
576.3.j.a 32 16.f odd 4 1
576.3.j.a 32 24.f even 2 1
576.3.j.a 32 48.k even 4 1
1152.3.j.a 32 1.a even 1 1 trivial
1152.3.j.a 32 3.b odd 2 1 inner
1152.3.j.a 32 16.e even 4 1 inner
1152.3.j.a 32 48.i odd 4 1 inner
1152.3.j.b 32 4.b odd 2 1
1152.3.j.b 32 12.b even 2 1
1152.3.j.b 32 16.f odd 4 1
1152.3.j.b 32 48.k even 4 1