Newspace parameters
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.m (of order \(5\), degree \(4\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(9.73531515095\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
16.1 | −1.73360 | − | 5.33547i | −2.42705 | − | 1.76336i | −18.9898 | + | 13.7969i | −1.54508 | + | 4.75528i | −5.20080 | + | 16.0064i | 24.0593 | − | 17.4801i | 70.2246 | + | 51.0211i | 2.78115 | + | 8.55951i | 28.0502 | ||
16.2 | −1.08489 | − | 3.33894i | −2.42705 | − | 1.76336i | −3.49938 | + | 2.54245i | −1.54508 | + | 4.75528i | −3.25466 | + | 10.0168i | −11.4322 | + | 8.30596i | −10.4366 | − | 7.58266i | 2.78115 | + | 8.55951i | 17.5538 | ||
16.3 | −0.914984 | − | 2.81603i | −2.42705 | − | 1.76336i | −0.620704 | + | 0.450968i | −1.54508 | + | 4.75528i | −2.74495 | + | 8.44810i | 20.5786 | − | 14.9512i | −17.3258 | − | 12.5879i | 2.78115 | + | 8.55951i | 14.8048 | ||
16.4 | 0.237147 | + | 0.729862i | −2.42705 | − | 1.76336i | 5.99568 | − | 4.35611i | −1.54508 | + | 4.75528i | 0.711440 | − | 2.18959i | 5.09134 | − | 3.69907i | 9.56808 | + | 6.95162i | 2.78115 | + | 8.55951i | −3.83711 | ||
16.5 | 0.609711 | + | 1.87650i | −2.42705 | − | 1.76336i | 3.32264 | − | 2.41404i | −1.54508 | + | 4.75528i | 1.82913 | − | 5.62949i | −13.8429 | + | 10.0574i | 19.3257 | + | 14.0410i | 2.78115 | + | 8.55951i | −9.86533 | ||
16.6 | 1.15055 | + | 3.54102i | −2.42705 | − | 1.76336i | −4.74290 | + | 3.44592i | −1.54508 | + | 4.75528i | 3.45164 | − | 10.6230i | −11.4369 | + | 8.30940i | 6.43837 | + | 4.67775i | 2.78115 | + | 8.55951i | −18.6162 | ||
31.1 | −1.73360 | + | 5.33547i | −2.42705 | + | 1.76336i | −18.9898 | − | 13.7969i | −1.54508 | − | 4.75528i | −5.20080 | − | 16.0064i | 24.0593 | + | 17.4801i | 70.2246 | − | 51.0211i | 2.78115 | − | 8.55951i | 28.0502 | ||
31.2 | −1.08489 | + | 3.33894i | −2.42705 | + | 1.76336i | −3.49938 | − | 2.54245i | −1.54508 | − | 4.75528i | −3.25466 | − | 10.0168i | −11.4322 | − | 8.30596i | −10.4366 | + | 7.58266i | 2.78115 | − | 8.55951i | 17.5538 | ||
31.3 | −0.914984 | + | 2.81603i | −2.42705 | + | 1.76336i | −0.620704 | − | 0.450968i | −1.54508 | − | 4.75528i | −2.74495 | − | 8.44810i | 20.5786 | + | 14.9512i | −17.3258 | + | 12.5879i | 2.78115 | − | 8.55951i | 14.8048 | ||
31.4 | 0.237147 | − | 0.729862i | −2.42705 | + | 1.76336i | 5.99568 | + | 4.35611i | −1.54508 | − | 4.75528i | 0.711440 | + | 2.18959i | 5.09134 | + | 3.69907i | 9.56808 | − | 6.95162i | 2.78115 | − | 8.55951i | −3.83711 | ||
31.5 | 0.609711 | − | 1.87650i | −2.42705 | + | 1.76336i | 3.32264 | + | 2.41404i | −1.54508 | − | 4.75528i | 1.82913 | + | 5.62949i | −13.8429 | − | 10.0574i | 19.3257 | − | 14.0410i | 2.78115 | − | 8.55951i | −9.86533 | ||
31.6 | 1.15055 | − | 3.54102i | −2.42705 | + | 1.76336i | −4.74290 | − | 3.44592i | −1.54508 | − | 4.75528i | 3.45164 | + | 10.6230i | −11.4369 | − | 8.30940i | 6.43837 | − | 4.67775i | 2.78115 | − | 8.55951i | −18.6162 | ||
91.1 | −3.76750 | + | 2.73725i | 0.927051 | + | 2.85317i | 4.22938 | − | 13.0167i | 4.04508 | + | 2.93893i | −11.3025 | − | 8.21174i | 1.04715 | − | 3.22280i | 8.18331 | + | 25.1856i | −7.28115 | + | 5.29007i | −23.2844 | ||
91.2 | −2.79760 | + | 2.03258i | 0.927051 | + | 2.85317i | 1.22307 | − | 3.76423i | 4.04508 | + | 2.93893i | −8.39281 | − | 6.09773i | −0.169994 | + | 0.523189i | −4.31930 | − | 13.2934i | −7.28115 | + | 5.29007i | −17.2901 | ||
91.3 | 0.0713397 | − | 0.0518313i | 0.927051 | + | 2.85317i | −2.46973 | + | 7.60106i | 4.04508 | + | 2.93893i | 0.214019 | + | 0.155494i | −6.20592 | + | 19.0999i | 0.435778 | + | 1.34119i | −7.28115 | + | 5.29007i | 0.440904 | ||
91.4 | 1.82807 | − | 1.32817i | 0.927051 | + | 2.85317i | −0.894328 | + | 2.75246i | 4.04508 | + | 2.93893i | 5.48422 | + | 3.98452i | 7.37247 | − | 22.6901i | 7.60694 | + | 23.4117i | −7.28115 | + | 5.29007i | 11.2981 | ||
91.5 | 3.00512 | − | 2.18335i | 0.927051 | + | 2.85317i | 1.79161 | − | 5.51401i | 4.04508 | + | 2.93893i | 9.01537 | + | 6.55005i | −6.55262 | + | 20.1669i | 2.52784 | + | 7.77988i | −7.28115 | + | 5.29007i | 18.5727 | ||
91.6 | 4.39663 | − | 3.19434i | 0.927051 | + | 2.85317i | 6.65444 | − | 20.4802i | 4.04508 | + | 2.93893i | 13.1899 | + | 9.58302i | 2.99170 | − | 9.20750i | −22.7289 | − | 69.9523i | −7.28115 | + | 5.29007i | 27.1727 | ||
136.1 | −3.76750 | − | 2.73725i | 0.927051 | − | 2.85317i | 4.22938 | + | 13.0167i | 4.04508 | − | 2.93893i | −11.3025 | + | 8.21174i | 1.04715 | + | 3.22280i | 8.18331 | − | 25.1856i | −7.28115 | − | 5.29007i | −23.2844 | ||
136.2 | −2.79760 | − | 2.03258i | 0.927051 | − | 2.85317i | 1.22307 | + | 3.76423i | 4.04508 | − | 2.93893i | −8.39281 | + | 6.09773i | −0.169994 | − | 0.523189i | −4.31930 | + | 13.2934i | −7.28115 | − | 5.29007i | −17.2901 | ||
See all 24 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
11.c | even | 5 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 165.4.m.d | ✓ | 24 |
11.c | even | 5 | 1 | inner | 165.4.m.d | ✓ | 24 |
11.c | even | 5 | 1 | 1815.4.a.bg | 12 | ||
11.d | odd | 10 | 1 | 1815.4.a.bo | 12 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
165.4.m.d | ✓ | 24 | 1.a | even | 1 | 1 | trivial |
165.4.m.d | ✓ | 24 | 11.c | even | 5 | 1 | inner |
1815.4.a.bg | 12 | 11.c | even | 5 | 1 | ||
1815.4.a.bo | 12 | 11.d | odd | 10 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{24} - 2 T_{2}^{23} + 34 T_{2}^{22} - 149 T_{2}^{21} + 1212 T_{2}^{20} - 1490 T_{2}^{19} + 31819 T_{2}^{18} - 68287 T_{2}^{17} + 658346 T_{2}^{16} - 1541489 T_{2}^{15} + 10159597 T_{2}^{14} - 22123599 T_{2}^{13} + \cdots + 453519616 \)
acting on \(S_{4}^{\mathrm{new}}(165, [\chi])\).