Properties

Label 1050.3.q.d
Level $1050$
Weight $3$
Character orbit 1050.q
Analytic conductor $28.610$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{4} - 36 q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{4} - 36 q^{9} - 8 q^{11} - 16 q^{14} - 48 q^{16} - 24 q^{19} + 36 q^{21} - 48 q^{26} + 48 q^{29} - 396 q^{31} - 144 q^{36} + 72 q^{39} + 16 q^{44} + 64 q^{46} - 56 q^{49} - 48 q^{51} + 80 q^{56} + 96 q^{59} + 372 q^{61} - 192 q^{64} + 72 q^{66} - 272 q^{71} + 128 q^{74} + 140 q^{79} - 108 q^{81} + 24 q^{84} - 416 q^{86} - 336 q^{89} + 584 q^{91} + 408 q^{94} + 48 q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
199.1 −1.22474 + 0.707107i −0.866025 + 1.50000i 1.00000 1.73205i 0 2.44949i 2.33475 6.59916i 2.82843i −1.50000 2.59808i 0
199.2 −1.22474 + 0.707107i 0.866025 1.50000i 1.00000 1.73205i 0 2.44949i −1.64177 6.80475i 2.82843i −1.50000 2.59808i 0
199.3 −1.22474 + 0.707107i −0.866025 + 1.50000i 1.00000 1.73205i 0 2.44949i −6.74171 1.88399i 2.82843i −1.50000 2.59808i 0
199.4 −1.22474 + 0.707107i 0.866025 1.50000i 1.00000 1.73205i 0 2.44949i 0.264136 + 6.99501i 2.82843i −1.50000 2.59808i 0
199.5 −1.22474 + 0.707107i 0.866025 1.50000i 1.00000 1.73205i 0 2.44949i 6.78392 1.72580i 2.82843i −1.50000 2.59808i 0
199.6 −1.22474 + 0.707107i −0.866025 + 1.50000i 1.00000 1.73205i 0 2.44949i 6.34914 + 2.94762i 2.82843i −1.50000 2.59808i 0
199.7 1.22474 0.707107i 0.866025 1.50000i 1.00000 1.73205i 0 2.44949i −2.33475 + 6.59916i 2.82843i −1.50000 2.59808i 0
199.8 1.22474 0.707107i −0.866025 + 1.50000i 1.00000 1.73205i 0 2.44949i 1.64177 + 6.80475i 2.82843i −1.50000 2.59808i 0
199.9 1.22474 0.707107i 0.866025 1.50000i 1.00000 1.73205i 0 2.44949i −6.34914 2.94762i 2.82843i −1.50000 2.59808i 0
199.10 1.22474 0.707107i −0.866025 + 1.50000i 1.00000 1.73205i 0 2.44949i −0.264136 6.99501i 2.82843i −1.50000 2.59808i 0
199.11 1.22474 0.707107i 0.866025 1.50000i 1.00000 1.73205i 0 2.44949i 6.74171 + 1.88399i 2.82843i −1.50000 2.59808i 0
199.12 1.22474 0.707107i −0.866025 + 1.50000i 1.00000 1.73205i 0 2.44949i −6.78392 + 1.72580i 2.82843i −1.50000 2.59808i 0
649.1 −1.22474 0.707107i −0.866025 1.50000i 1.00000 + 1.73205i 0 2.44949i 2.33475 + 6.59916i 2.82843i −1.50000 + 2.59808i 0
649.2 −1.22474 0.707107i 0.866025 + 1.50000i 1.00000 + 1.73205i 0 2.44949i −1.64177 + 6.80475i 2.82843i −1.50000 + 2.59808i 0
649.3 −1.22474 0.707107i −0.866025 1.50000i 1.00000 + 1.73205i 0 2.44949i −6.74171 + 1.88399i 2.82843i −1.50000 + 2.59808i 0
649.4 −1.22474 0.707107i 0.866025 + 1.50000i 1.00000 + 1.73205i 0 2.44949i 0.264136 6.99501i 2.82843i −1.50000 + 2.59808i 0
649.5 −1.22474 0.707107i 0.866025 + 1.50000i 1.00000 + 1.73205i 0 2.44949i 6.78392 + 1.72580i 2.82843i −1.50000 + 2.59808i 0
649.6 −1.22474 0.707107i −0.866025 1.50000i 1.00000 + 1.73205i 0 2.44949i 6.34914 2.94762i 2.82843i −1.50000 + 2.59808i 0
649.7 1.22474 + 0.707107i 0.866025 + 1.50000i 1.00000 + 1.73205i 0 2.44949i −2.33475 6.59916i 2.82843i −1.50000 + 2.59808i 0
649.8 1.22474 + 0.707107i −0.866025 1.50000i 1.00000 + 1.73205i 0 2.44949i 1.64177 6.80475i 2.82843i −1.50000 + 2.59808i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 649.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
7.d odd 6 1 inner
35.i odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1050.3.q.d 24
5.b even 2 1 inner 1050.3.q.d 24
5.c odd 4 1 1050.3.p.e 12
5.c odd 4 1 1050.3.p.f yes 12
7.d odd 6 1 inner 1050.3.q.d 24
35.i odd 6 1 inner 1050.3.q.d 24
35.k even 12 1 1050.3.p.e 12
35.k even 12 1 1050.3.p.f yes 12
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1050.3.p.e 12 5.c odd 4 1
1050.3.p.e 12 35.k even 12 1
1050.3.p.f yes 12 5.c odd 4 1
1050.3.p.f yes 12 35.k even 12 1
1050.3.q.d 24 1.a even 1 1 trivial
1050.3.q.d 24 5.b even 2 1 inner
1050.3.q.d 24 7.d odd 6 1 inner
1050.3.q.d 24 35.i odd 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{11}^{12} + \cdots\) acting on \(S_{3}^{\mathrm{new}}(1050, [\chi])\).