Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 2\sqrt{19}\).
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.
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{2} - 20 T_{2} + 24 \) acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(5))\).
| $p$ |
$F_p(T)$ |
| $2$
| \( 1 - 20 T + 280 T^{2} - 2560 T^{3} + 16384 T^{4} \)
|
| $3$
| \( 1 - 20 T - 390 T^{2} - 43740 T^{3} + 4782969 T^{4} \)
|
| $5$
| \( ( 1 + 125 T )^{2} \)
|
| $7$
| \( 1 + 100 T + 1411250 T^{2} + 82354300 T^{3} + 678223072849 T^{4} \)
|
| $11$
| \( 1 - 4544 T + 31976326 T^{2} - 88549705024 T^{3} + 379749833583241 T^{4} \)
|
| $13$
| \( 1 - 3540 T + 100535470 T^{2} - 222129750180 T^{3} + 3937376385699289 T^{4} \)
|
| $17$
| \( 1 + 27340 T + 901005190 T^{2} + 11218659319820 T^{3} + 168377826559400929 T^{4} \)
|
| $19$
| \( 1 - 38760 T + 2155545478 T^{2} - 34646468603640 T^{3} + 799006685782884121 T^{4} \)
|
| $23$
| \( 1 + 124140 T + 10649684530 T^{2} + 422675030990580 T^{3} + 11592836324538749809 T^{4} \)
|
| $29$
| \( 1 + 72260 T + 6846819118 T^{2} + 1246476062088340 T^{3} + \)\(29\!\cdots\!81\)\( T^{4} \)
|
| $31$
| \( 1 - 306824 T + 77964629966 T^{2} - 8441530311993464 T^{3} + \)\(75\!\cdots\!21\)\( T^{4} \)
|
| $37$
| \( 1 + 123020 T + 144088599870 T^{2} + 11678519524901660 T^{3} + \)\(90\!\cdots\!89\)\( T^{4} \)
|
| $41$
| \( 1 - 264364 T + 161786388886 T^{2} - 51486018860276684 T^{3} + \)\(37\!\cdots\!61\)\( T^{4} \)
|
| $43$
| \( 1 - 423300 T + 446651231050 T^{2} - 115060818081593100 T^{3} + \)\(73\!\cdots\!49\)\( T^{4} \)
|
| $47$
| \( 1 + 105460 T + 858715356610 T^{2} + 53428474284027980 T^{3} + \)\(25\!\cdots\!69\)\( T^{4} \)
|
| $53$
| \( 1 + 2391580 T + 3562552504510 T^{2} + 2809415667811372460 T^{3} + \)\(13\!\cdots\!69\)\( T^{4} \)
|
| $59$
| \( 1 + 1120120 T + 1362334883638 T^{2} + 2787588301175458280 T^{3} + \)\(61\!\cdots\!61\)\( T^{4} \)
|
| $61$
| \( 1 - 2257044 T + 5613447576526 T^{2} - 7093308861584181924 T^{3} + \)\(98\!\cdots\!41\)\( T^{4} \)
|
| $67$
| \( 1 - 4516460 T + 16742087664890 T^{2} - 27372961536977116580 T^{3} + \)\(36\!\cdots\!29\)\( T^{4} \)
|
| $71$
| \( 1 - 621784 T + 17914494152446 T^{2} - 5655200192564989544 T^{3} + \)\(82\!\cdots\!81\)\( T^{4} \)
|
| $73$
| \( 1 - 4569060 T + 23424949855030 T^{2} - 50476226677665338820 T^{3} + \)\(12\!\cdots\!09\)\( T^{4} \)
|
| $79$
| \( 1 - 4333040 T + 26135588252318 T^{2} - 83211305793386393360 T^{3} + \)\(36\!\cdots\!81\)\( T^{4} \)
|
| $83$
| \( 1 + 9793020 T + 59971104320890 T^{2} + \)\(26\!\cdots\!40\)\( T^{3} + \)\(73\!\cdots\!29\)\( T^{4} \)
|
| $89$
| \( 1 - 6025620 T + 89865866149558 T^{2} - \)\(26\!\cdots\!80\)\( T^{3} + \)\(19\!\cdots\!41\)\( T^{4} \)
|
| $97$
| \( 1 - 4609540 T + 142930351581510 T^{2} - \)\(37\!\cdots\!20\)\( T^{3} + \)\(65\!\cdots\!69\)\( T^{4} \)
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