Newspace parameters
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
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 | −2.65342 | 1.00000 | 5.04066 | 4.09935 | −2.65342 | 1.00000 | −8.06816 | 1.00000 | −10.8773 | ||||||||||||||||||
1.2 | −2.52420 | 1.00000 | 4.37157 | −0.338133 | −2.52420 | 1.00000 | −5.98631 | 1.00000 | 0.853514 | ||||||||||||||||||
1.3 | −2.42203 | 1.00000 | 3.86625 | 1.50568 | −2.42203 | 1.00000 | −4.52011 | 1.00000 | −3.64681 | ||||||||||||||||||
1.4 | −1.70789 | 1.00000 | 0.916895 | 2.36693 | −1.70789 | 1.00000 | 1.84983 | 1.00000 | −4.04246 | ||||||||||||||||||
1.5 | −1.69492 | 1.00000 | 0.872752 | −3.19478 | −1.69492 | 1.00000 | 1.91059 | 1.00000 | 5.41490 | ||||||||||||||||||
1.6 | −1.64011 | 1.00000 | 0.689959 | −1.40502 | −1.64011 | 1.00000 | 2.14861 | 1.00000 | 2.30438 | ||||||||||||||||||
1.7 | −1.28891 | 1.00000 | −0.338712 | 0.716613 | −1.28891 | 1.00000 | 3.01439 | 1.00000 | −0.923650 | ||||||||||||||||||
1.8 | −1.05296 | 1.00000 | −0.891266 | 4.03535 | −1.05296 | 1.00000 | 3.04440 | 1.00000 | −4.24908 | ||||||||||||||||||
1.9 | −0.768548 | 1.00000 | −1.40933 | 3.25090 | −0.768548 | 1.00000 | 2.62024 | 1.00000 | −2.49847 | ||||||||||||||||||
1.10 | −0.667457 | 1.00000 | −1.55450 | −3.08787 | −0.667457 | 1.00000 | 2.37248 | 1.00000 | 2.06102 | ||||||||||||||||||
1.11 | −0.105370 | 1.00000 | −1.98890 | −1.28706 | −0.105370 | 1.00000 | 0.420311 | 1.00000 | 0.135618 | ||||||||||||||||||
1.12 | −0.0599798 | 1.00000 | −1.99640 | 3.32796 | −0.0599798 | 1.00000 | 0.239704 | 1.00000 | −0.199610 | ||||||||||||||||||
1.13 | 0.267433 | 1.00000 | −1.92848 | 0.0366447 | 0.267433 | 1.00000 | −1.05060 | 1.00000 | 0.00980000 | ||||||||||||||||||
1.14 | 0.374739 | 1.00000 | −1.85957 | 2.21215 | 0.374739 | 1.00000 | −1.44633 | 1.00000 | 0.828982 | ||||||||||||||||||
1.15 | 0.640778 | 1.00000 | −1.58940 | −2.69509 | 0.640778 | 1.00000 | −2.30001 | 1.00000 | −1.72696 | ||||||||||||||||||
1.16 | 1.25182 | 1.00000 | −0.432954 | 2.68317 | 1.25182 | 1.00000 | −3.04561 | 1.00000 | 3.35884 | ||||||||||||||||||
1.17 | 1.25557 | 1.00000 | −0.423542 | 3.43059 | 1.25557 | 1.00000 | −3.04293 | 1.00000 | 4.30735 | ||||||||||||||||||
1.18 | 1.40876 | 1.00000 | −0.0154013 | −2.50452 | 1.40876 | 1.00000 | −2.83921 | 1.00000 | −3.52826 | ||||||||||||||||||
1.19 | 1.44666 | 1.00000 | 0.0928390 | 2.29705 | 1.44666 | 1.00000 | −2.75902 | 1.00000 | 3.32306 | ||||||||||||||||||
1.20 | 1.74433 | 1.00000 | 1.04268 | −1.87140 | 1.74433 | 1.00000 | −1.66989 | 1.00000 | −3.26434 | ||||||||||||||||||
See all 27 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(7\) | \(-1\) |
\(191\) | \(-1\) |
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 | 4011.2.a.k | ✓ | 27 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4011.2.a.k | ✓ | 27 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{27} - 9 T_{2}^{26} - 2 T_{2}^{25} + 243 T_{2}^{24} - 493 T_{2}^{23} - 2496 T_{2}^{22} + 8759 T_{2}^{21} + 10702 T_{2}^{20} - 70333 T_{2}^{19} + 2142 T_{2}^{18} + 318278 T_{2}^{17} - 221040 T_{2}^{16} - 857364 T_{2}^{15} + \cdots - 64 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\).