Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{2}\).
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
|
| \(3\) |
\(1\) |
| \(5\) |
\(-1\) |
| \(7\) |
\(1\) |
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{2} + 2 T_{2} - 7 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(105))\).
Hecke Characteristic Polynomials
| $p$ |
$F_p(T)$ |
| $2$
| \( 1 + 2 T + 9 T^{2} + 16 T^{3} + 64 T^{4} \)
|
| $3$
| \( ( 1 + 3 T )^{2} \)
|
| $5$
| \( ( 1 - 5 T )^{2} \)
|
| $7$
| \( ( 1 + 7 T )^{2} \)
|
| $11$
| \( 1 + 16 T - 474 T^{2} + 21296 T^{3} + 1771561 T^{4} \)
|
| $13$
| \( 1 + 76 T + 5806 T^{2} + 166972 T^{3} + 4826809 T^{4} \)
|
| $17$
| \( 1 + 124 T + 13638 T^{2} + 609212 T^{3} + 24137569 T^{4} \)
|
| $19$
| \( 1 + 96 T + 13974 T^{2} + 658464 T^{3} + 47045881 T^{4} \)
|
| $23$
| \( 1 + 16 T + 15150 T^{2} + 194672 T^{3} + 148035889 T^{4} \)
|
| $29$
| \( 1 - 188 T + 34286 T^{2} - 4585132 T^{3} + 594823321 T^{4} \)
|
| $31$
| \( 1 + 120 T + 60590 T^{2} + 3574920 T^{3} + 887503681 T^{4} \)
|
| $37$
| \( 1 + 132 T + 70814 T^{2} + 6686196 T^{3} + 2565726409 T^{4} \)
|
| $41$
| \( 1 - 100 T + 89142 T^{2} - 6892100 T^{3} + 4750104241 T^{4} \)
|
| $43$
| \( 1 + 536 T + 200086 T^{2} + 42615752 T^{3} + 6321363049 T^{4} \)
|
| $47$
| \( 1 + 928 T + 408830 T^{2} + 96347744 T^{3} + 10779215329 T^{4} \)
|
| $53$
| \( 1 - 884 T + 460350 T^{2} - 131607268 T^{3} + 22164361129 T^{4} \)
|
| $59$
| \( 1 - 104 T + 80534 T^{2} - 21359416 T^{3} + 42180533641 T^{4} \)
|
| $61$
| \( 1 + 468 T + 494606 T^{2} + 106227108 T^{3} + 51520374361 T^{4} \)
|
| $67$
| \( 1 + 1688 T + 1302310 T^{2} + 507687944 T^{3} + 90458382169 T^{4} \)
|
| $71$
| \( 1 + 136 T + 540446 T^{2} + 48675896 T^{3} + 128100283921 T^{4} \)
|
| $73$
| \( 1 - 508 T + 13078 T^{2} - 197620636 T^{3} + 151334226289 T^{4} \)
|
| $79$
| \( 1 + 432 T + 602142 T^{2} + 212992848 T^{3} + 243087455521 T^{4} \)
|
| $83$
| \( 1 + 584 T + 1172390 T^{2} + 333923608 T^{3} + 326940373369 T^{4} \)
|
| $89$
| \( 1 + 1404 T + 1802390 T^{2} + 989776476 T^{3} + 496981290961 T^{4} \)
|
| $97$
| \( 1 + 1188 T + 2161254 T^{2} + 1084255524 T^{3} + 832972004929 T^{4} \)
|
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