Newspace parameters
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (of order \(4\), degree \(2\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
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.
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
191.1 | −0.707107 | − | 0.707107i | 0.169604 | − | 1.72373i | 1.00000i | 0.707107 | − | 0.707107i | −1.33879 | + | 1.09893i | 1.82689 | 0.707107 | − | 0.707107i | −2.94247 | − | 0.584702i | −1.00000 | ||||||
191.2 | −0.707107 | − | 0.707107i | −0.392697 | − | 1.68695i | 1.00000i | 0.707107 | − | 0.707107i | −0.915172 | + | 1.47053i | −0.873718 | 0.707107 | − | 0.707107i | −2.69158 | + | 1.32492i | −1.00000 | ||||||
191.3 | −0.707107 | − | 0.707107i | 0.125486 | + | 1.72750i | 1.00000i | 0.707107 | − | 0.707107i | 1.13279 | − | 1.31026i | 0.386861 | 0.707107 | − | 0.707107i | −2.96851 | + | 0.433555i | −1.00000 | ||||||
191.4 | −0.707107 | − | 0.707107i | −0.912090 | − | 1.47244i | 1.00000i | 0.707107 | − | 0.707107i | −0.396230 | + | 1.68612i | −2.79858 | 0.707107 | − | 0.707107i | −1.33618 | + | 2.68600i | −1.00000 | ||||||
191.5 | −0.707107 | − | 0.707107i | 1.33218 | + | 1.10694i | 1.00000i | 0.707107 | − | 0.707107i | −0.159268 | − | 1.72471i | −3.17089 | 0.707107 | − | 0.707107i | 0.549384 | + | 2.94927i | −1.00000 | ||||||
191.6 | −0.707107 | − | 0.707107i | −0.407565 | + | 1.68342i | 1.00000i | 0.707107 | − | 0.707107i | 1.47855 | − | 0.902163i | 2.94059 | 0.707107 | − | 0.707107i | −2.66778 | − | 1.37220i | −1.00000 | ||||||
191.7 | −0.707107 | − | 0.707107i | 1.70946 | + | 0.278802i | 1.00000i | 0.707107 | − | 0.707107i | −1.01163 | − | 1.40592i | −0.348034 | 0.707107 | − | 0.707107i | 2.84454 | + | 0.953204i | −1.00000 | ||||||
191.8 | −0.707107 | − | 0.707107i | −1.72452 | − | 0.161390i | 1.00000i | 0.707107 | − | 0.707107i | 1.10530 | + | 1.33354i | 0.212791 | 0.707107 | − | 0.707107i | 2.94791 | + | 0.556641i | −1.00000 | ||||||
191.9 | −0.707107 | − | 0.707107i | 1.65121 | − | 0.522966i | 1.00000i | 0.707107 | − | 0.707107i | −1.53738 | − | 0.797792i | 3.44243 | 0.707107 | − | 0.707107i | 2.45301 | − | 1.72706i | −1.00000 | ||||||
191.10 | −0.707107 | − | 0.707107i | −1.55108 | + | 0.770820i | 1.00000i | 0.707107 | − | 0.707107i | 1.64183 | + | 0.551724i | 4.38167 | 0.707107 | − | 0.707107i | 1.81167 | − | 2.39120i | −1.00000 | ||||||
191.11 | 0.707107 | + | 0.707107i | −1.33218 | + | 1.10694i | 1.00000i | −0.707107 | + | 0.707107i | −1.72471 | − | 0.159268i | −3.17089 | −0.707107 | + | 0.707107i | 0.549384 | − | 2.94927i | −1.00000 | ||||||
191.12 | 0.707107 | + | 0.707107i | 0.912090 | − | 1.47244i | 1.00000i | −0.707107 | + | 0.707107i | 1.68612 | − | 0.396230i | −2.79858 | −0.707107 | + | 0.707107i | −1.33618 | − | 2.68600i | −1.00000 | ||||||
191.13 | 0.707107 | + | 0.707107i | −1.70946 | + | 0.278802i | 1.00000i | −0.707107 | + | 0.707107i | −1.40592 | − | 1.01163i | −0.348034 | −0.707107 | + | 0.707107i | 2.84454 | − | 0.953204i | −1.00000 | ||||||
191.14 | 0.707107 | + | 0.707107i | 0.392697 | − | 1.68695i | 1.00000i | −0.707107 | + | 0.707107i | 1.47053 | − | 0.915172i | −0.873718 | −0.707107 | + | 0.707107i | −2.69158 | − | 1.32492i | −1.00000 | ||||||
191.15 | 0.707107 | + | 0.707107i | −1.65121 | − | 0.522966i | 1.00000i | −0.707107 | + | 0.707107i | −0.797792 | − | 1.53738i | 3.44243 | −0.707107 | + | 0.707107i | 2.45301 | + | 1.72706i | −1.00000 | ||||||
191.16 | 0.707107 | + | 0.707107i | −0.125486 | + | 1.72750i | 1.00000i | −0.707107 | + | 0.707107i | −1.31026 | + | 1.13279i | 0.386861 | −0.707107 | + | 0.707107i | −2.96851 | − | 0.433555i | −1.00000 | ||||||
191.17 | 0.707107 | + | 0.707107i | 1.55108 | + | 0.770820i | 1.00000i | −0.707107 | + | 0.707107i | 0.551724 | + | 1.64183i | 4.38167 | −0.707107 | + | 0.707107i | 1.81167 | + | 2.39120i | −1.00000 | ||||||
191.18 | 0.707107 | + | 0.707107i | −0.169604 | − | 1.72373i | 1.00000i | −0.707107 | + | 0.707107i | 1.09893 | − | 1.33879i | 1.82689 | −0.707107 | + | 0.707107i | −2.94247 | + | 0.584702i | −1.00000 | ||||||
191.19 | 0.707107 | + | 0.707107i | 1.72452 | − | 0.161390i | 1.00000i | −0.707107 | + | 0.707107i | 1.33354 | + | 1.10530i | 0.212791 | −0.707107 | + | 0.707107i | 2.94791 | − | 0.556641i | −1.00000 | ||||||
191.20 | 0.707107 | + | 0.707107i | 0.407565 | + | 1.68342i | 1.00000i | −0.707107 | + | 0.707107i | −0.902163 | + | 1.47855i | 2.94059 | −0.707107 | + | 0.707107i | −2.66778 | + | 1.37220i | −1.00000 | ||||||
See all 40 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
3.b | odd | 2 | 1 | inner |
37.d | odd | 4 | 1 | inner |
111.g | even | 4 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1110.2.u.f | ✓ | 40 |
3.b | odd | 2 | 1 | inner | 1110.2.u.f | ✓ | 40 |
37.d | odd | 4 | 1 | inner | 1110.2.u.f | ✓ | 40 |
111.g | even | 4 | 1 | inner | 1110.2.u.f | ✓ | 40 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1110.2.u.f | ✓ | 40 | 1.a | even | 1 | 1 | trivial |
1110.2.u.f | ✓ | 40 | 3.b | odd | 2 | 1 | inner |
1110.2.u.f | ✓ | 40 | 37.d | odd | 4 | 1 | inner |
1110.2.u.f | ✓ | 40 | 111.g | even | 4 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \(T_{7}^{10} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(1110, [\chi])\).