Newspace parameters
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.z (of order \(10\), degree \(4\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(2.19588605559\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
49.1 | −2.63006 | + | 0.854560i | 0.964848 | − | 1.32800i | 4.56893 | − | 3.31953i | 0 | −1.40276 | + | 4.31724i | 1.11557 | + | 1.53545i | −5.92892 | + | 8.16046i | 0.0944009 | + | 0.290536i | 0 | ||||
49.2 | −1.59020 | + | 0.516686i | −1.82798 | + | 2.51599i | 0.643729 | − | 0.467696i | 0 | 1.60686 | − | 4.94542i | −1.81624 | − | 2.49985i | 1.18359 | − | 1.62907i | −2.06168 | − | 6.34519i | 0 | ||||
49.3 | −0.911888 | + | 0.296290i | 0.528620 | − | 0.727583i | −0.874283 | + | 0.635204i | 0 | −0.266466 | + | 0.820099i | −0.447684 | − | 0.616184i | 1.73620 | − | 2.38967i | 0.677113 | + | 2.08394i | 0 | ||||
49.4 | −0.132580 | + | 0.0430779i | 1.75502 | − | 2.41558i | −1.60231 | + | 1.16415i | 0 | −0.128623 | + | 0.395861i | −2.09815 | − | 2.88786i | 0.326164 | − | 0.448926i | −1.82787 | − | 5.62561i | 0 | ||||
49.5 | 0.132580 | − | 0.0430779i | −1.75502 | + | 2.41558i | −1.60231 | + | 1.16415i | 0 | −0.128623 | + | 0.395861i | 2.09815 | + | 2.88786i | −0.326164 | + | 0.448926i | −1.82787 | − | 5.62561i | 0 | ||||
49.6 | 0.911888 | − | 0.296290i | −0.528620 | + | 0.727583i | −0.874283 | + | 0.635204i | 0 | −0.266466 | + | 0.820099i | 0.447684 | + | 0.616184i | −1.73620 | + | 2.38967i | 0.677113 | + | 2.08394i | 0 | ||||
49.7 | 1.59020 | − | 0.516686i | 1.82798 | − | 2.51599i | 0.643729 | − | 0.467696i | 0 | 1.60686 | − | 4.94542i | 1.81624 | + | 2.49985i | −1.18359 | + | 1.62907i | −2.06168 | − | 6.34519i | 0 | ||||
49.8 | 2.63006 | − | 0.854560i | −0.964848 | + | 1.32800i | 4.56893 | − | 3.31953i | 0 | −1.40276 | + | 4.31724i | −1.11557 | − | 1.53545i | 5.92892 | − | 8.16046i | 0.0944009 | + | 0.290536i | 0 | ||||
124.1 | −1.50618 | − | 2.07308i | 1.70486 | − | 0.553942i | −1.41105 | + | 4.34277i | 0 | −3.71620 | − | 2.69998i | 3.61485 | + | 1.17454i | 6.25410 | − | 2.03208i | 0.172643 | − | 0.125433i | 0 | ||||
124.2 | −1.34829 | − | 1.85576i | 0.0403304 | − | 0.0131041i | −1.00792 | + | 3.10207i | 0 | −0.0786950 | − | 0.0571753i | −1.08390 | − | 0.352180i | 2.75251 | − | 0.894346i | −2.42560 | + | 1.76230i | 0 | ||||
124.3 | −0.776830 | − | 1.06921i | −1.92724 | + | 0.626199i | 0.0782786 | − | 0.240917i | 0 | 2.16668 | + | 1.57419i | 0.331213 | + | 0.107618i | −2.83228 | + | 0.920262i | 0.895086 | − | 0.650318i | 0 | ||||
124.4 | −0.122427 | − | 0.168506i | −1.80155 | + | 0.585361i | 0.604628 | − | 1.86085i | 0 | 0.319195 | + | 0.231909i | 1.22573 | + | 0.398265i | −0.783769 | + | 0.254662i | 0.475901 | − | 0.345762i | 0 | ||||
124.5 | 0.122427 | + | 0.168506i | 1.80155 | − | 0.585361i | 0.604628 | − | 1.86085i | 0 | 0.319195 | + | 0.231909i | −1.22573 | − | 0.398265i | 0.783769 | − | 0.254662i | 0.475901 | − | 0.345762i | 0 | ||||
124.6 | 0.776830 | + | 1.06921i | 1.92724 | − | 0.626199i | 0.0782786 | − | 0.240917i | 0 | 2.16668 | + | 1.57419i | −0.331213 | − | 0.107618i | 2.83228 | − | 0.920262i | 0.895086 | − | 0.650318i | 0 | ||||
124.7 | 1.34829 | + | 1.85576i | −0.0403304 | + | 0.0131041i | −1.00792 | + | 3.10207i | 0 | −0.0786950 | − | 0.0571753i | 1.08390 | + | 0.352180i | −2.75251 | + | 0.894346i | −2.42560 | + | 1.76230i | 0 | ||||
124.8 | 1.50618 | + | 2.07308i | −1.70486 | + | 0.553942i | −1.41105 | + | 4.34277i | 0 | −3.71620 | − | 2.69998i | −3.61485 | − | 1.17454i | −6.25410 | + | 2.03208i | 0.172643 | − | 0.125433i | 0 | ||||
174.1 | −2.63006 | − | 0.854560i | 0.964848 | + | 1.32800i | 4.56893 | + | 3.31953i | 0 | −1.40276 | − | 4.31724i | 1.11557 | − | 1.53545i | −5.92892 | − | 8.16046i | 0.0944009 | − | 0.290536i | 0 | ||||
174.2 | −1.59020 | − | 0.516686i | −1.82798 | − | 2.51599i | 0.643729 | + | 0.467696i | 0 | 1.60686 | + | 4.94542i | −1.81624 | + | 2.49985i | 1.18359 | + | 1.62907i | −2.06168 | + | 6.34519i | 0 | ||||
174.3 | −0.911888 | − | 0.296290i | 0.528620 | + | 0.727583i | −0.874283 | − | 0.635204i | 0 | −0.266466 | − | 0.820099i | −0.447684 | + | 0.616184i | 1.73620 | + | 2.38967i | 0.677113 | − | 2.08394i | 0 | ||||
174.4 | −0.132580 | − | 0.0430779i | 1.75502 | + | 2.41558i | −1.60231 | − | 1.16415i | 0 | −0.128623 | − | 0.395861i | −2.09815 | + | 2.88786i | 0.326164 | + | 0.448926i | −1.82787 | + | 5.62561i | 0 | ||||
See all 32 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
5.b | even | 2 | 1 | inner |
11.c | even | 5 | 1 | inner |
55.j | even | 10 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 275.2.z.c | 32 | |
5.b | even | 2 | 1 | inner | 275.2.z.c | 32 | |
5.c | odd | 4 | 1 | 275.2.h.c | ✓ | 16 | |
5.c | odd | 4 | 1 | 275.2.h.e | yes | 16 | |
11.c | even | 5 | 1 | inner | 275.2.z.c | 32 | |
55.j | even | 10 | 1 | inner | 275.2.z.c | 32 | |
55.k | odd | 20 | 1 | 275.2.h.c | ✓ | 16 | |
55.k | odd | 20 | 1 | 275.2.h.e | yes | 16 | |
55.k | odd | 20 | 1 | 3025.2.a.bi | 8 | ||
55.k | odd | 20 | 1 | 3025.2.a.bn | 8 | ||
55.l | even | 20 | 1 | 3025.2.a.bj | 8 | ||
55.l | even | 20 | 1 | 3025.2.a.bm | 8 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
275.2.h.c | ✓ | 16 | 5.c | odd | 4 | 1 | |
275.2.h.c | ✓ | 16 | 55.k | odd | 20 | 1 | |
275.2.h.e | yes | 16 | 5.c | odd | 4 | 1 | |
275.2.h.e | yes | 16 | 55.k | odd | 20 | 1 | |
275.2.z.c | 32 | 1.a | even | 1 | 1 | trivial | |
275.2.z.c | 32 | 5.b | even | 2 | 1 | inner | |
275.2.z.c | 32 | 11.c | even | 5 | 1 | inner | |
275.2.z.c | 32 | 55.j | even | 10 | 1 | inner | |
3025.2.a.bi | 8 | 55.k | odd | 20 | 1 | ||
3025.2.a.bj | 8 | 55.l | even | 20 | 1 | ||
3025.2.a.bm | 8 | 55.l | even | 20 | 1 | ||
3025.2.a.bn | 8 | 55.k | odd | 20 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{32} - 10 T_{2}^{30} + 89 T_{2}^{28} - 694 T_{2}^{26} + 5502 T_{2}^{24} - 20142 T_{2}^{22} + 113853 T_{2}^{20} - 411465 T_{2}^{18} + 961802 T_{2}^{16} - 1330529 T_{2}^{14} + 2642317 T_{2}^{12} - 2806839 T_{2}^{10} + \cdots + 1 \)
acting on \(S_{2}^{\mathrm{new}}(275, [\chi])\).