Newspace parameters
Level: | \( N \) | \(=\) | \( 1205 = 5 \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1205.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(9.62197344356\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
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 | −2.73903 | 2.66987 | 5.50229 | 1.00000 | −7.31286 | 4.66369 | −9.59289 | 4.12822 | −2.73903 | ||||||||||||||||||
1.2 | −2.51976 | −0.981670 | 4.34921 | 1.00000 | 2.47358 | 3.43036 | −5.91946 | −2.03632 | −2.51976 | ||||||||||||||||||
1.3 | −2.18227 | 2.05137 | 2.76228 | 1.00000 | −4.47663 | −1.39304 | −1.66351 | 1.20812 | −2.18227 | ||||||||||||||||||
1.4 | −2.14165 | −1.43070 | 2.58667 | 1.00000 | 3.06405 | −0.0457027 | −1.25644 | −0.953111 | −2.14165 | ||||||||||||||||||
1.5 | −1.83164 | 0.379920 | 1.35491 | 1.00000 | −0.695877 | −4.92875 | 1.18157 | −2.85566 | −1.83164 | ||||||||||||||||||
1.6 | −1.58885 | 2.11200 | 0.524458 | 1.00000 | −3.35566 | 3.95616 | 2.34442 | 1.46053 | −1.58885 | ||||||||||||||||||
1.7 | −1.25748 | −2.42991 | −0.418732 | 1.00000 | 3.05557 | 3.44014 | 3.04152 | 2.90444 | −1.25748 | ||||||||||||||||||
1.8 | −1.16007 | 2.40515 | −0.654229 | 1.00000 | −2.79015 | 1.39900 | 3.07910 | 2.78474 | −1.16007 | ||||||||||||||||||
1.9 | −1.11717 | 3.26371 | −0.751931 | 1.00000 | −3.64612 | −3.89846 | 3.07438 | 7.65181 | −1.11717 | ||||||||||||||||||
1.10 | −0.566303 | −0.484852 | −1.67930 | 1.00000 | 0.274573 | −0.0113879 | 2.08360 | −2.76492 | −0.566303 | ||||||||||||||||||
1.11 | −0.0694400 | −2.28670 | −1.99518 | 1.00000 | 0.158789 | 0.976003 | 0.277425 | 2.22902 | −0.0694400 | ||||||||||||||||||
1.12 | 0.300307 | 0.482693 | −1.90982 | 1.00000 | 0.144956 | 5.09571 | −1.17415 | −2.76701 | 0.300307 | ||||||||||||||||||
1.13 | 0.362712 | 3.41577 | −1.86844 | 1.00000 | 1.23894 | 3.34046 | −1.40313 | 8.66752 | 0.362712 | ||||||||||||||||||
1.14 | 0.707449 | 1.14949 | −1.49952 | 1.00000 | 0.813204 | 1.94091 | −2.47573 | −1.67868 | 0.707449 | ||||||||||||||||||
1.15 | 0.782724 | −1.54504 | −1.38734 | 1.00000 | −1.20934 | −2.90223 | −2.65136 | −0.612841 | 0.782724 | ||||||||||||||||||
1.16 | 1.05446 | 2.79403 | −0.888118 | 1.00000 | 2.94619 | −1.63707 | −3.04540 | 4.80663 | 1.05446 | ||||||||||||||||||
1.17 | 1.31571 | −0.792486 | −0.268903 | 1.00000 | −1.04268 | −1.49796 | −2.98522 | −2.37197 | 1.31571 | ||||||||||||||||||
1.18 | 1.91059 | 2.10440 | 1.65034 | 1.00000 | 4.02063 | 2.16427 | −0.668063 | 1.42849 | 1.91059 | ||||||||||||||||||
1.19 | 1.96718 | 2.44636 | 1.86979 | 1.00000 | 4.81242 | 2.28114 | −0.256155 | 2.98466 | 1.96718 | ||||||||||||||||||
1.20 | 2.03980 | −3.04377 | 2.16080 | 1.00000 | −6.20869 | 3.73609 | 0.327997 | 6.26453 | 2.03980 | ||||||||||||||||||
See all 25 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(5\) | \(-1\) |
\(241\) | \(1\) |
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 | 1205.2.a.e | ✓ | 25 |
5.b | even | 2 | 1 | 6025.2.a.j | 25 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1205.2.a.e | ✓ | 25 | 1.a | even | 1 | 1 | trivial |
6025.2.a.j | 25 | 5.b | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{25} - 6 T_{2}^{24} - 23 T_{2}^{23} + 197 T_{2}^{22} + 127 T_{2}^{21} - 2741 T_{2}^{20} + 1209 T_{2}^{19} + 21093 T_{2}^{18} - 21526 T_{2}^{17} - 98096 T_{2}^{16} + 140217 T_{2}^{15} + 281530 T_{2}^{14} - 511289 T_{2}^{13} + \cdots + 409 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1205))\).