Newspace parameters
Level: | \( N \) | \(=\) | \( 6015 = 3 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6015.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(48.0300168158\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
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 | −2.62638 | 1.00000 | 4.89789 | 1.00000 | −2.62638 | −0.417980 | −7.61099 | 1.00000 | −2.62638 | ||||||||||||||||||
1.2 | −2.46180 | 1.00000 | 4.06045 | 1.00000 | −2.46180 | −1.67554 | −5.07240 | 1.00000 | −2.46180 | ||||||||||||||||||
1.3 | −2.22931 | 1.00000 | 2.96981 | 1.00000 | −2.22931 | −0.230360 | −2.16201 | 1.00000 | −2.22931 | ||||||||||||||||||
1.4 | −2.14529 | 1.00000 | 2.60225 | 1.00000 | −2.14529 | −2.89107 | −1.29200 | 1.00000 | −2.14529 | ||||||||||||||||||
1.5 | −1.79507 | 1.00000 | 1.22228 | 1.00000 | −1.79507 | 3.49730 | 1.39607 | 1.00000 | −1.79507 | ||||||||||||||||||
1.6 | −1.63766 | 1.00000 | 0.681937 | 1.00000 | −1.63766 | −0.197583 | 2.15854 | 1.00000 | −1.63766 | ||||||||||||||||||
1.7 | −1.27466 | 1.00000 | −0.375250 | 1.00000 | −1.27466 | −0.831191 | 3.02763 | 1.00000 | −1.27466 | ||||||||||||||||||
1.8 | −1.13202 | 1.00000 | −0.718528 | 1.00000 | −1.13202 | −1.31252 | 3.07743 | 1.00000 | −1.13202 | ||||||||||||||||||
1.9 | −1.12824 | 1.00000 | −0.727075 | 1.00000 | −1.12824 | −4.89351 | 3.07679 | 1.00000 | −1.12824 | ||||||||||||||||||
1.10 | −0.791085 | 1.00000 | −1.37418 | 1.00000 | −0.791085 | 2.45382 | 2.66927 | 1.00000 | −0.791085 | ||||||||||||||||||
1.11 | −0.762017 | 1.00000 | −1.41933 | 1.00000 | −0.762017 | 2.32113 | 2.60559 | 1.00000 | −0.762017 | ||||||||||||||||||
1.12 | −0.108293 | 1.00000 | −1.98827 | 1.00000 | −0.108293 | −2.69972 | 0.431901 | 1.00000 | −0.108293 | ||||||||||||||||||
1.13 | 0.0493063 | 1.00000 | −1.99757 | 1.00000 | 0.0493063 | 2.05010 | −0.197105 | 1.00000 | 0.0493063 | ||||||||||||||||||
1.14 | 0.186838 | 1.00000 | −1.96509 | 1.00000 | 0.186838 | −4.07485 | −0.740831 | 1.00000 | 0.186838 | ||||||||||||||||||
1.15 | 0.592282 | 1.00000 | −1.64920 | 1.00000 | 0.592282 | −0.542800 | −2.16136 | 1.00000 | 0.592282 | ||||||||||||||||||
1.16 | 0.783438 | 1.00000 | −1.38623 | 1.00000 | 0.783438 | −0.845679 | −2.65290 | 1.00000 | 0.783438 | ||||||||||||||||||
1.17 | 1.02584 | 1.00000 | −0.947645 | 1.00000 | 1.02584 | 0.748026 | −3.02382 | 1.00000 | 1.02584 | ||||||||||||||||||
1.18 | 1.03713 | 1.00000 | −0.924357 | 1.00000 | 1.03713 | 2.93887 | −3.03294 | 1.00000 | 1.03713 | ||||||||||||||||||
1.19 | 1.60756 | 1.00000 | 0.584262 | 1.00000 | 1.60756 | 0.859599 | −2.27589 | 1.00000 | 1.60756 | ||||||||||||||||||
1.20 | 1.75959 | 1.00000 | 1.09616 | 1.00000 | 1.75959 | −3.35674 | −1.59039 | 1.00000 | 1.75959 | ||||||||||||||||||
See all 23 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(5\) | \(-1\) |
\(401\) | \(1\) |
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 | 6015.2.a.b | ✓ | 23 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6015.2.a.b | ✓ | 23 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{23} + 5 T_{2}^{22} - 15 T_{2}^{21} - 106 T_{2}^{20} + 57 T_{2}^{19} + 942 T_{2}^{18} + 252 T_{2}^{17} - 4580 T_{2}^{16} - 3018 T_{2}^{15} + 13334 T_{2}^{14} + 11792 T_{2}^{13} - 23949 T_{2}^{12} - 24531 T_{2}^{11} + 26491 T_{2}^{10} + \cdots - 1 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6015))\).