Newspace parameters
Level: | \( N \) | \(=\) | \( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1140.bo (of order \(9\), degree \(6\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(9.10294583043\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
61.1 | 0 | 0.173648 | + | 0.984808i | 0 | 0.766044 | − | 0.642788i | 0 | −1.88256 | + | 3.26069i | 0 | −0.939693 | + | 0.342020i | 0 | ||||||||||
61.2 | 0 | 0.173648 | + | 0.984808i | 0 | 0.766044 | − | 0.642788i | 0 | −1.63777 | + | 2.83669i | 0 | −0.939693 | + | 0.342020i | 0 | ||||||||||
61.3 | 0 | 0.173648 | + | 0.984808i | 0 | 0.766044 | − | 0.642788i | 0 | 0.671715 | − | 1.16344i | 0 | −0.939693 | + | 0.342020i | 0 | ||||||||||
61.4 | 0 | 0.173648 | + | 0.984808i | 0 | 0.766044 | − | 0.642788i | 0 | 0.908917 | − | 1.57429i | 0 | −0.939693 | + | 0.342020i | 0 | ||||||||||
301.1 | 0 | −0.939693 | + | 0.342020i | 0 | 0.173648 | − | 0.984808i | 0 | −1.72562 | − | 2.98886i | 0 | 0.766044 | − | 0.642788i | 0 | ||||||||||
301.2 | 0 | −0.939693 | + | 0.342020i | 0 | 0.173648 | − | 0.984808i | 0 | −1.49396 | − | 2.58762i | 0 | 0.766044 | − | 0.642788i | 0 | ||||||||||
301.3 | 0 | −0.939693 | + | 0.342020i | 0 | 0.173648 | − | 0.984808i | 0 | 0.802800 | + | 1.39049i | 0 | 0.766044 | − | 0.642788i | 0 | ||||||||||
301.4 | 0 | −0.939693 | + | 0.342020i | 0 | 0.173648 | − | 0.984808i | 0 | 2.18283 | + | 3.78077i | 0 | 0.766044 | − | 0.642788i | 0 | ||||||||||
481.1 | 0 | −0.939693 | − | 0.342020i | 0 | 0.173648 | + | 0.984808i | 0 | −1.72562 | + | 2.98886i | 0 | 0.766044 | + | 0.642788i | 0 | ||||||||||
481.2 | 0 | −0.939693 | − | 0.342020i | 0 | 0.173648 | + | 0.984808i | 0 | −1.49396 | + | 2.58762i | 0 | 0.766044 | + | 0.642788i | 0 | ||||||||||
481.3 | 0 | −0.939693 | − | 0.342020i | 0 | 0.173648 | + | 0.984808i | 0 | 0.802800 | − | 1.39049i | 0 | 0.766044 | + | 0.642788i | 0 | ||||||||||
481.4 | 0 | −0.939693 | − | 0.342020i | 0 | 0.173648 | + | 0.984808i | 0 | 2.18283 | − | 3.78077i | 0 | 0.766044 | + | 0.642788i | 0 | ||||||||||
541.1 | 0 | 0.766044 | − | 0.642788i | 0 | −0.939693 | − | 0.342020i | 0 | −1.59457 | + | 2.76187i | 0 | 0.173648 | − | 0.984808i | 0 | ||||||||||
541.2 | 0 | 0.766044 | − | 0.642788i | 0 | −0.939693 | − | 0.342020i | 0 | −1.35032 | + | 2.33882i | 0 | 0.173648 | − | 0.984808i | 0 | ||||||||||
541.3 | 0 | 0.766044 | − | 0.642788i | 0 | −0.939693 | − | 0.342020i | 0 | −0.00547393 | + | 0.00948113i | 0 | 0.173648 | − | 0.984808i | 0 | ||||||||||
541.4 | 0 | 0.766044 | − | 0.642788i | 0 | −0.939693 | − | 0.342020i | 0 | 2.12401 | − | 3.67889i | 0 | 0.173648 | − | 0.984808i | 0 | ||||||||||
841.1 | 0 | 0.173648 | − | 0.984808i | 0 | 0.766044 | + | 0.642788i | 0 | −1.88256 | − | 3.26069i | 0 | −0.939693 | − | 0.342020i | 0 | ||||||||||
841.2 | 0 | 0.173648 | − | 0.984808i | 0 | 0.766044 | + | 0.642788i | 0 | −1.63777 | − | 2.83669i | 0 | −0.939693 | − | 0.342020i | 0 | ||||||||||
841.3 | 0 | 0.173648 | − | 0.984808i | 0 | 0.766044 | + | 0.642788i | 0 | 0.671715 | + | 1.16344i | 0 | −0.939693 | − | 0.342020i | 0 | ||||||||||
841.4 | 0 | 0.173648 | − | 0.984808i | 0 | 0.766044 | + | 0.642788i | 0 | 0.908917 | + | 1.57429i | 0 | −0.939693 | − | 0.342020i | 0 | ||||||||||
See all 24 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
19.e | even | 9 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1140.2.bo.c | ✓ | 24 |
19.e | even | 9 | 1 | inner | 1140.2.bo.c | ✓ | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1140.2.bo.c | ✓ | 24 | 1.a | even | 1 | 1 | trivial |
1140.2.bo.c | ✓ | 24 | 19.e | even | 9 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7}^{24} + 6 T_{7}^{23} + 72 T_{7}^{22} + 336 T_{7}^{21} + 2691 T_{7}^{20} + 11001 T_{7}^{19} + 64658 T_{7}^{18} + 218331 T_{7}^{17} + 1028043 T_{7}^{16} + 2904099 T_{7}^{15} + 11270763 T_{7}^{14} + 24386904 T_{7}^{13} + \cdots + 760384 \)
acting on \(S_{2}^{\mathrm{new}}(1140, [\chi])\).