Newspace parameters
Level: | \( N \) | \(=\) | \( 1007 = 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1007.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(8.04093548354\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.1 | −2.79936 | −0.556375 | 5.83643 | 3.29617 | 1.55750 | 1.71230 | −10.7396 | −2.69045 | −9.22719 | ||||||||||||||||||
1.2 | −2.53366 | −2.25575 | 4.41941 | −2.33573 | 5.71528 | 4.14311 | −6.12995 | 2.08839 | 5.91795 | ||||||||||||||||||
1.3 | −2.38950 | 1.62577 | 3.70970 | −3.78025 | −3.88478 | 0.614408 | −4.08532 | −0.356869 | 9.03289 | ||||||||||||||||||
1.4 | −2.38706 | 0.0564175 | 3.69805 | −1.85429 | −0.134672 | −3.74665 | −4.05333 | −2.99682 | 4.42631 | ||||||||||||||||||
1.5 | −2.34547 | 2.87039 | 3.50124 | 4.42818 | −6.73242 | −0.392048 | −3.52111 | 5.23914 | −10.3862 | ||||||||||||||||||
1.6 | −1.68252 | −3.19593 | 0.830859 | −3.54229 | 5.37720 | 2.49260 | 1.96710 | 7.21397 | 5.95996 | ||||||||||||||||||
1.7 | −1.51529 | −3.16005 | 0.296109 | 2.95244 | 4.78840 | 0.224928 | 2.58189 | 6.98592 | −4.47381 | ||||||||||||||||||
1.8 | −1.43121 | 2.80880 | 0.0483583 | −0.613402 | −4.01997 | 5.06624 | 2.79321 | 4.88934 | 0.877906 | ||||||||||||||||||
1.9 | −1.24731 | 2.80833 | −0.444220 | 3.12412 | −3.50286 | −0.445019 | 3.04870 | 4.88673 | −3.89675 | ||||||||||||||||||
1.10 | −1.00515 | −0.139424 | −0.989678 | 2.93604 | 0.140142 | 2.04416 | 3.00507 | −2.98056 | −2.95115 | ||||||||||||||||||
1.11 | −0.948115 | −1.20576 | −1.10108 | 0.444866 | 1.14320 | −2.45657 | 2.94018 | −1.54613 | −0.421784 | ||||||||||||||||||
1.12 | −0.791316 | 1.08394 | −1.37382 | −3.99094 | −0.857740 | −4.54351 | 2.66976 | −1.82507 | 3.15810 | ||||||||||||||||||
1.13 | −0.319045 | −0.935679 | −1.89821 | −2.32921 | 0.298524 | 0.376334 | 1.24371 | −2.12451 | 0.743125 | ||||||||||||||||||
1.14 | 0.180018 | 1.16800 | −1.96759 | 0.0855821 | 0.210261 | 3.31494 | −0.714240 | −1.63579 | 0.0154064 | ||||||||||||||||||
1.15 | 0.541632 | 2.77685 | −1.70664 | 2.24627 | 1.50403 | −2.00794 | −2.00763 | 4.71088 | 1.21665 | ||||||||||||||||||
1.16 | 0.570474 | −3.28720 | −1.67456 | 2.69142 | −1.87526 | 5.04218 | −2.09624 | 7.80570 | 1.53539 | ||||||||||||||||||
1.17 | 0.758750 | −2.46973 | −1.42430 | 3.84414 | −1.87391 | −4.23932 | −2.59819 | 3.09957 | 2.91675 | ||||||||||||||||||
1.18 | 0.896802 | −1.02005 | −1.19575 | −1.65827 | −0.914780 | −3.83554 | −2.86595 | −1.95950 | −1.48714 | ||||||||||||||||||
1.19 | 1.26121 | 1.79187 | −0.409342 | 2.69609 | 2.25993 | 2.95821 | −3.03869 | 0.210786 | 3.40035 | ||||||||||||||||||
1.20 | 1.28042 | −1.37836 | −0.360526 | −3.13293 | −1.76487 | 4.02144 | −3.02246 | −1.10014 | −4.01147 | ||||||||||||||||||
See all 28 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(19\) | \(1\) |
\(53\) | \(-1\) |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1007.2.a.e | ✓ | 28 |
3.b | odd | 2 | 1 | 9063.2.a.r | 28 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1007.2.a.e | ✓ | 28 | 1.a | even | 1 | 1 | trivial |
9063.2.a.r | 28 | 3.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{28} - 3 T_{2}^{27} - 42 T_{2}^{26} + 128 T_{2}^{25} + 773 T_{2}^{24} - 2398 T_{2}^{23} - 8210 T_{2}^{22} + 25984 T_{2}^{21} + 55795 T_{2}^{20} - 180640 T_{2}^{19} - 254355 T_{2}^{18} + 845427 T_{2}^{17} + 792781 T_{2}^{16} + \cdots - 5878 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1007))\).