Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{57})\).
We also show the integral \(q\)-expansion of the trace form.
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.
This newform does not admit any (nontrivial) inner twists.
| \( p \) |
Sign
|
| \(7\) |
\(-1\) |
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(49))\):
| \( T_{2}^{2} - 9 T_{2} + 6 \) |
| \( T_{3}^{2} - 6 T_{3} - 504 \) |
| $p$ |
$F_p(T)$ |
| $2$
| \( 1 - 9 T + 70 T^{2} - 288 T^{3} + 1024 T^{4} \)
|
| $3$
| \( 1 - 6 T - 18 T^{2} - 1458 T^{3} + 59049 T^{4} \)
|
| $5$
| \( 1 - 18 T + 4906 T^{2} - 56250 T^{3} + 9765625 T^{4} \)
|
| $7$
| 1
|
| $11$
| \( 1 - 396 T + 142198 T^{2} - 63776196 T^{3} + 25937424601 T^{4} \)
|
| $13$
| \( 1 - 350 T + 546978 T^{2} - 129952550 T^{3} + 137858491849 T^{4} \)
|
| $17$
| \( 1 + 1800 T + 3567406 T^{2} + 2555742600 T^{3} + 2015993900449 T^{4} \)
|
| $19$
| \( 1 - 3266 T + 7614270 T^{2} - 8086939334 T^{3} + 6131066257801 T^{4} \)
|
| $23$
| \( 1 - 2088 T + 9365230 T^{2} - 13439084184 T^{3} + 41426511213649 T^{4} \)
|
| $29$
| \( 1 - 6696 T + 51326470 T^{2} - 137342653704 T^{3} + 420707233300201 T^{4} \)
|
| $31$
| \( 1 - 20 T + 53103102 T^{2} - 572583020 T^{3} + 819628286980801 T^{4} \)
|
| $37$
| \( 1 - 6232 T + 144242070 T^{2} - 432151540024 T^{3} + 4808584372417849 T^{4} \)
|
| $41$
| \( 1 - 6048 T + 223864366 T^{2} - 700698303648 T^{3} + 13422659310152401 T^{4} \)
|
| $43$
| \( 1 + 3020 T - 30383466 T^{2} + 443965497860 T^{3} + 21611482313284249 T^{4} \)
|
| $47$
| \( 1 + 11700 T + 292735582 T^{2} + 2683336581900 T^{3} + 52599132235830049 T^{4} \)
|
| $53$
| \( 1 - 9468 T + 858185230 T^{2} - 3959474927724 T^{3} + 174887470365513049 T^{4} \)
|
| $59$
| \( 1 - 43938 T + 1852599934 T^{2} - 31412343849462 T^{3} + 511116753300641401 T^{4} \)
|
| $61$
| \( 1 - 64754 T + 2408321418 T^{2} - 54690988874954 T^{3} + 713342911662882601 T^{4} \)
|
| $67$
| \( 1 - 24784 T + 2799959190 T^{2} - 33461500651888 T^{3} + 1822837804551761449 T^{4} \)
|
| $71$
| \( 1 - 97416 T + 5729557966 T^{2} - 175760806457016 T^{3} + 3255243551009881201 T^{4} \)
|
| $73$
| \( 1 + 17452 T + 3828622374 T^{2} + 36179245441036 T^{3} + 4297625829703557649 T^{4} \)
|
| $79$
| \( 1 - 51256 T + 3645565854 T^{2} - 157717602787144 T^{3} + 9468276082626847201 T^{4} \)
|
| $83$
| \( 1 + 117558 T + 7798161502 T^{2} + 463065739909794 T^{3} + 15516041187205853449 T^{4} \)
|
| $89$
| \( 1 + 84276 T + 5915697430 T^{2} + 470602194123924 T^{3} + 31181719929966183601 T^{4} \)
|
| $97$
| \( 1 + 20776 T + 16174049358 T^{2} + 178410581179432 T^{3} + 73742412689492826049 T^{4} \)
|
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