Properties

Label 1148.2.a
Level 1148
Weight 2
Character orbit a
Rep. character \(\chi_{1148}(1,\cdot)\)
Character field \(\Q\)
Dimension 20
Newform subspaces 5
Sturm bound 336
Trace bound 5

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(336\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1148))\).

Total New Old
Modular forms 174 20 154
Cusp forms 163 20 143
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(7\)\(41\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(10\)
Minus space\(-\)\(10\)

Trace form

\( 20q - 4q^{3} - 4q^{5} + 12q^{9} + O(q^{10}) \) \( 20q - 4q^{3} - 4q^{5} + 12q^{9} + 8q^{15} - 4q^{17} - 4q^{19} - 4q^{21} + 8q^{23} + 8q^{25} - 4q^{27} + 4q^{29} + 8q^{31} + 16q^{33} + 4q^{35} - 20q^{37} + 28q^{39} - 4q^{43} - 4q^{45} - 8q^{47} + 20q^{49} - 20q^{51} + 8q^{53} - 24q^{55} - 4q^{57} - 20q^{59} - 28q^{61} + 8q^{63} - 4q^{65} - 24q^{67} + 44q^{69} - 4q^{71} - 20q^{73} - 52q^{75} - 8q^{77} + 4q^{79} + 12q^{81} - 8q^{83} - 40q^{85} - 44q^{87} - 16q^{89} - 12q^{91} + 16q^{93} - 16q^{95} - 4q^{97} - 36q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1148))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 41
1148.2.a.a \(2\) \(9.167\) \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(-3\) \(2\) \(-\) \(-\) \(+\) \(q+(-1-\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+\cdots\)
1148.2.a.b \(3\) \(9.167\) \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(0\) \(3\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-2\beta _{1}+2\beta _{2})q^{5}+\cdots\)
1148.2.a.c \(5\) \(9.167\) 5.5.470117.1 None \(0\) \(-2\) \(-1\) \(-5\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}-q^{7}+\cdots\)
1148.2.a.d \(5\) \(9.167\) 5.5.287349.1 None \(0\) \(2\) \(-3\) \(-5\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}-q^{7}+\cdots\)
1148.2.a.e \(5\) \(9.167\) 5.5.1935333.1 None \(0\) \(2\) \(3\) \(5\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1148))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1148)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 3 T + 5 T^{2} + 9 T^{3} + 9 T^{4} \))(\( 1 + 3 T + 9 T^{2} + 15 T^{3} + 27 T^{4} + 27 T^{5} + 27 T^{6} \))(\( 1 + 2 T + 9 T^{2} + 16 T^{3} + 43 T^{4} + 59 T^{5} + 129 T^{6} + 144 T^{7} + 243 T^{8} + 162 T^{9} + 243 T^{10} \))(\( 1 - 2 T + 9 T^{2} - 16 T^{3} + 45 T^{4} - 59 T^{5} + 135 T^{6} - 144 T^{7} + 243 T^{8} - 162 T^{9} + 243 T^{10} \))(\( 1 - 2 T + 7 T^{2} - 14 T^{3} + 31 T^{4} - 59 T^{5} + 93 T^{6} - 126 T^{7} + 189 T^{8} - 162 T^{9} + 243 T^{10} \))
$5$ (\( 1 + 3 T + 9 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 + 3 T^{2} - 8 T^{3} + 15 T^{4} + 125 T^{6} \))(\( 1 + T + 16 T^{2} + 12 T^{3} + 127 T^{4} + 78 T^{5} + 635 T^{6} + 300 T^{7} + 2000 T^{8} + 625 T^{9} + 3125 T^{10} \))(\( 1 + 3 T + 16 T^{2} + 48 T^{3} + 143 T^{4} + 322 T^{5} + 715 T^{6} + 1200 T^{7} + 2000 T^{8} + 1875 T^{9} + 3125 T^{10} \))(\( 1 - 3 T + 16 T^{2} - 40 T^{3} + 127 T^{4} - 274 T^{5} + 635 T^{6} - 1000 T^{7} + 2000 T^{8} - 1875 T^{9} + 3125 T^{10} \))
$7$ (\( ( 1 - T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{5} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))
$11$ (\( ( 1 - T + 11 T^{2} )^{2} \))(\( 1 + 6 T + 9 T^{2} - 4 T^{3} + 99 T^{4} + 726 T^{5} + 1331 T^{6} \))(\( 1 + 2 T + 26 T^{2} - 10 T^{3} + 165 T^{4} - 728 T^{5} + 1815 T^{6} - 1210 T^{7} + 34606 T^{8} + 29282 T^{9} + 161051 T^{10} \))(\( 1 - 6 T + 48 T^{2} - 196 T^{3} + 895 T^{4} - 2836 T^{5} + 9845 T^{6} - 23716 T^{7} + 63888 T^{8} - 87846 T^{9} + 161051 T^{10} \))(\( 1 + 34 T^{2} + 4 T^{3} + 601 T^{4} + 16 T^{5} + 6611 T^{6} + 484 T^{7} + 45254 T^{8} + 161051 T^{10} \))
$13$ (\( ( 1 + 5 T + 13 T^{2} )^{2} \))(\( 1 + 3 T + 21 T^{2} + 21 T^{3} + 273 T^{4} + 507 T^{5} + 2197 T^{6} \))(\( 1 + T + 42 T^{2} + 4 T^{3} + 835 T^{4} - 131 T^{5} + 10855 T^{6} + 676 T^{7} + 92274 T^{8} + 28561 T^{9} + 371293 T^{10} \))(\( 1 - 7 T + 60 T^{2} - 328 T^{3} + 1513 T^{4} - 6189 T^{5} + 19669 T^{6} - 55432 T^{7} + 131820 T^{8} - 199927 T^{9} + 371293 T^{10} \))(\( 1 - 7 T + 72 T^{2} - 326 T^{3} + 1883 T^{4} - 6081 T^{5} + 24479 T^{6} - 55094 T^{7} + 158184 T^{8} - 199927 T^{9} + 371293 T^{10} \))
$17$ (\( 1 + 2 T - 17 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 - 3 T + 51 T^{2} - 99 T^{3} + 867 T^{4} - 867 T^{5} + 4913 T^{6} \))(\( 1 + 3 T + 56 T^{2} + 126 T^{3} + 1591 T^{4} + 3013 T^{5} + 27047 T^{6} + 36414 T^{7} + 275128 T^{8} + 250563 T^{9} + 1419857 T^{10} \))(\( 1 - T + 68 T^{2} - 82 T^{3} + 2041 T^{4} - 2209 T^{5} + 34697 T^{6} - 23698 T^{7} + 334084 T^{8} - 83521 T^{9} + 1419857 T^{10} \))(\( 1 + 3 T + 40 T^{2} + 132 T^{3} + 1135 T^{4} + 2835 T^{5} + 19295 T^{6} + 38148 T^{7} + 196520 T^{8} + 250563 T^{9} + 1419857 T^{10} \))
$19$ (\( 1 + 3 T + 11 T^{2} + 57 T^{3} + 361 T^{4} \))(\( 1 + 9 T + 63 T^{2} + 269 T^{3} + 1197 T^{4} + 3249 T^{5} + 6859 T^{6} \))(\( 1 + 4 T + 39 T^{2} + 48 T^{3} + 441 T^{4} - 365 T^{5} + 8379 T^{6} + 17328 T^{7} + 267501 T^{8} + 521284 T^{9} + 2476099 T^{10} \))(\( 1 - 2 T + 27 T^{2} + 24 T^{3} + 901 T^{4} - 1287 T^{5} + 17119 T^{6} + 8664 T^{7} + 185193 T^{8} - 260642 T^{9} + 2476099 T^{10} \))(\( 1 - 10 T + 117 T^{2} - 730 T^{3} + 4783 T^{4} - 20523 T^{5} + 90877 T^{6} - 263530 T^{7} + 802503 T^{8} - 1303210 T^{9} + 2476099 T^{10} \))
$23$ (\( 1 + 3 T + 45 T^{2} + 69 T^{3} + 529 T^{4} \))(\( 1 - 3 T + 51 T^{2} - 101 T^{3} + 1173 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 + 8 T + 83 T^{2} + 574 T^{3} + 3355 T^{4} + 18011 T^{5} + 77165 T^{6} + 303646 T^{7} + 1009861 T^{8} + 2238728 T^{9} + 6436343 T^{10} \))(\( 1 - 4 T + 23 T^{2} - 58 T^{3} + 1051 T^{4} - 4157 T^{5} + 24173 T^{6} - 30682 T^{7} + 279841 T^{8} - 1119364 T^{9} + 6436343 T^{10} \))(\( 1 - 12 T + 163 T^{2} - 1174 T^{3} + 8623 T^{4} - 41305 T^{5} + 198329 T^{6} - 621046 T^{7} + 1983221 T^{8} - 3358092 T^{9} + 6436343 T^{10} \))
$29$ (\( 1 - 17 T + 127 T^{2} - 493 T^{3} + 841 T^{4} \))(\( 1 + 12 T + 123 T^{2} + 704 T^{3} + 3567 T^{4} + 10092 T^{5} + 24389 T^{6} \))(\( 1 + 9 T + 68 T^{2} + 24 T^{3} - 1301 T^{4} - 16106 T^{5} - 37729 T^{6} + 20184 T^{7} + 1658452 T^{8} + 6365529 T^{9} + 20511149 T^{10} \))(\( 1 - 11 T + 114 T^{2} - 876 T^{3} + 6109 T^{4} - 32522 T^{5} + 177161 T^{6} - 736716 T^{7} + 2780346 T^{8} - 7780091 T^{9} + 20511149 T^{10} \))(\( 1 + 3 T + 124 T^{2} + 284 T^{3} + 6667 T^{4} + 11690 T^{5} + 193343 T^{6} + 238844 T^{7} + 3024236 T^{8} + 2121843 T^{9} + 20511149 T^{10} \))
$31$ (\( 1 - 11 T + 63 T^{2} - 341 T^{3} + 961 T^{4} \))(\( 1 + 12 T + 93 T^{2} + 552 T^{3} + 2883 T^{4} + 11532 T^{5} + 29791 T^{6} \))(\( 1 + 11 T + 112 T^{2} + 656 T^{3} + 5003 T^{4} + 25610 T^{5} + 155093 T^{6} + 630416 T^{7} + 3336592 T^{8} + 10158731 T^{9} + 28629151 T^{10} \))(\( 1 - 13 T + 130 T^{2} - 830 T^{3} + 4765 T^{4} - 25298 T^{5} + 147715 T^{6} - 797630 T^{7} + 3872830 T^{8} - 12005773 T^{9} + 28629151 T^{10} \))(\( 1 - 7 T + 162 T^{2} - 842 T^{3} + 10229 T^{4} - 38742 T^{5} + 317099 T^{6} - 809162 T^{7} + 4826142 T^{8} - 6464647 T^{9} + 28629151 T^{10} \))
$37$ (\( 1 - 6 T + 70 T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 + 21 T + 237 T^{2} + 1733 T^{3} + 8769 T^{4} + 28749 T^{5} + 50653 T^{6} \))(\( 1 + 11 T + 145 T^{2} + 663 T^{3} + 4956 T^{4} + 12852 T^{5} + 183372 T^{6} + 907647 T^{7} + 7344685 T^{8} + 20615771 T^{9} + 69343957 T^{10} \))(\( 1 - 5 T + 117 T^{2} - 517 T^{3} + 6812 T^{4} - 26316 T^{5} + 252044 T^{6} - 707773 T^{7} + 5926401 T^{8} - 9370805 T^{9} + 69343957 T^{10} \))(\( 1 - T + 129 T^{2} - 293 T^{3} + 7484 T^{4} - 18756 T^{5} + 276908 T^{6} - 401117 T^{7} + 6534237 T^{8} - 1874161 T^{9} + 69343957 T^{10} \))
$41$ (\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))
$43$ (\( 1 + 16 T + 137 T^{2} + 688 T^{3} + 1849 T^{4} \))(\( 1 + 3 T + 93 T^{2} + 239 T^{3} + 3999 T^{4} + 5547 T^{5} + 79507 T^{6} \))(\( 1 + 27 T + 382 T^{2} + 3986 T^{3} + 34437 T^{4} + 248301 T^{5} + 1480791 T^{6} + 7370114 T^{7} + 30371674 T^{8} + 92307627 T^{9} + 147008443 T^{10} \))(\( 1 - 29 T + 522 T^{2} - 6438 T^{3} + 61101 T^{4} - 448587 T^{5} + 2627343 T^{6} - 11903862 T^{7} + 41502654 T^{8} - 99145229 T^{9} + 147008443 T^{10} \))(\( 1 - 13 T + 234 T^{2} - 2046 T^{3} + 20829 T^{4} - 128475 T^{5} + 895647 T^{6} - 3783054 T^{7} + 18604638 T^{8} - 44444413 T^{9} + 147008443 T^{10} \))
$47$ (\( 1 + 18 T + 162 T^{2} + 846 T^{3} + 2209 T^{4} \))(\( 1 + 3 T + 51 T^{2} - 99 T^{3} + 2397 T^{4} + 6627 T^{5} + 103823 T^{6} \))(\( 1 + 3 T + 167 T^{2} + 461 T^{3} + 13280 T^{4} + 29348 T^{5} + 624160 T^{6} + 1018349 T^{7} + 17338441 T^{8} + 14639043 T^{9} + 229345007 T^{10} \))(\( 1 - 7 T + 161 T^{2} - 1027 T^{3} + 12666 T^{4} - 67144 T^{5} + 595302 T^{6} - 2268643 T^{7} + 16715503 T^{8} - 34157767 T^{9} + 229345007 T^{10} \))(\( 1 - 9 T + 169 T^{2} - 1585 T^{3} + 12862 T^{4} - 109216 T^{5} + 604514 T^{6} - 3501265 T^{7} + 17546087 T^{8} - 43917129 T^{9} + 229345007 T^{10} \))
$53$ (\( 1 + 9 T + 123 T^{2} + 477 T^{3} + 2809 T^{4} \))(\( 1 - 18 T + 231 T^{2} - 1980 T^{3} + 12243 T^{4} - 50562 T^{5} + 148877 T^{6} \))(\( 1 + 19 T + 298 T^{2} + 2774 T^{3} + 25329 T^{4} + 175326 T^{5} + 1342437 T^{6} + 7792166 T^{7} + 44365346 T^{8} + 149919139 T^{9} + 418195493 T^{10} \))(\( 1 - 21 T + 354 T^{2} - 4212 T^{3} + 41957 T^{4} - 328646 T^{5} + 2223721 T^{6} - 11831508 T^{7} + 52702458 T^{8} - 165700101 T^{9} + 418195493 T^{10} \))(\( 1 + 3 T + 256 T^{2} + 616 T^{3} + 26671 T^{4} + 48466 T^{5} + 1413563 T^{6} + 1730344 T^{7} + 38112512 T^{8} + 23671443 T^{9} + 418195493 T^{10} \))
$59$ (\( 1 - T + 89 T^{2} - 59 T^{3} + 3481 T^{4} \))(\( 1 + 6 T + 141 T^{2} + 556 T^{3} + 8319 T^{4} + 20886 T^{5} + 205379 T^{6} \))(\( 1 + 15 T + 316 T^{2} + 3050 T^{3} + 36379 T^{4} + 253030 T^{5} + 2146361 T^{6} + 10617050 T^{7} + 64899764 T^{8} + 181760415 T^{9} + 714924299 T^{10} \))(\( 1 - 3 T + 32 T^{2} - 122 T^{3} + 2667 T^{4} - 48958 T^{5} + 157353 T^{6} - 424682 T^{7} + 6572128 T^{8} - 36352083 T^{9} + 714924299 T^{10} \))(\( 1 + 3 T + 208 T^{2} + 530 T^{3} + 20587 T^{4} + 40862 T^{5} + 1214633 T^{6} + 1844930 T^{7} + 42718832 T^{8} + 36352083 T^{9} + 714924299 T^{10} \))
$61$ (\( 1 + 6 T + 79 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 + 30 T + 471 T^{2} + 4532 T^{3} + 28731 T^{4} + 111630 T^{5} + 226981 T^{6} \))(\( 1 + 190 T^{2} - 30 T^{3} + 18957 T^{4} - 5364 T^{5} + 1156377 T^{6} - 111630 T^{7} + 43126390 T^{8} + 844596301 T^{10} \))(\( 1 + 8 T + 138 T^{2} + 1074 T^{3} + 13585 T^{4} + 83436 T^{5} + 828685 T^{6} + 3996354 T^{7} + 31323378 T^{8} + 110766728 T^{9} + 844596301 T^{10} \))(\( 1 - 16 T + 174 T^{2} - 270 T^{3} - 7827 T^{4} + 122124 T^{5} - 477447 T^{6} - 1004670 T^{7} + 39494694 T^{8} - 221533456 T^{9} + 844596301 T^{10} \))
$67$ (\( 1 + 7 T + 117 T^{2} + 469 T^{3} + 4489 T^{4} \))(\( 1 + 18 T + 261 T^{2} + 2276 T^{3} + 17487 T^{4} + 80802 T^{5} + 300763 T^{6} \))(\( 1 + 21 T + 310 T^{2} + 3174 T^{3} + 31197 T^{4} + 258962 T^{5} + 2090199 T^{6} + 14248086 T^{7} + 93236530 T^{8} + 423173541 T^{9} + 1350125107 T^{10} \))(\( 1 - 3 T - 10 T^{2} - 696 T^{3} + 4469 T^{4} - 15122 T^{5} + 299423 T^{6} - 3124344 T^{7} - 3007630 T^{8} - 60453363 T^{9} + 1350125107 T^{10} \))(\( 1 - 19 T + 360 T^{2} - 4400 T^{3} + 48887 T^{4} - 419922 T^{5} + 3275429 T^{6} - 19751600 T^{7} + 108274680 T^{8} - 382871299 T^{9} + 1350125107 T^{10} \))
$71$ (\( 1 + 10 T + 115 T^{2} + 710 T^{3} + 5041 T^{4} \))(\( 1 - 12 T + 177 T^{2} - 1728 T^{3} + 12567 T^{4} - 60492 T^{5} + 357911 T^{6} \))(\( 1 + 16 T + 338 T^{2} + 4312 T^{3} + 46713 T^{4} + 451448 T^{5} + 3316623 T^{6} + 21736792 T^{7} + 120973918 T^{8} + 406586896 T^{9} + 1804229351 T^{10} \))(\( 1 - 22 T + 152 T^{2} - 652 T^{3} + 13507 T^{4} - 179324 T^{5} + 958997 T^{6} - 3286732 T^{7} + 54402472 T^{8} - 559056982 T^{9} + 1804229351 T^{10} \))(\( 1 + 12 T + 286 T^{2} + 2964 T^{3} + 35425 T^{4} + 300480 T^{5} + 2515175 T^{6} + 14941524 T^{7} + 102362546 T^{8} + 304940172 T^{9} + 1804229351 T^{10} \))
$73$ (\( ( 1 - 7 T + 73 T^{2} )^{2} \))(\( 1 + 12 T + 219 T^{2} + 1688 T^{3} + 15987 T^{4} + 63948 T^{5} + 389017 T^{6} \))(\( 1 + 10 T + 222 T^{2} + 2492 T^{3} + 25941 T^{4} + 257572 T^{5} + 1893693 T^{6} + 13279868 T^{7} + 86361774 T^{8} + 283982410 T^{9} + 2073071593 T^{10} \))(\( 1 + 16 T + 338 T^{2} + 4158 T^{3} + 47185 T^{4} + 439204 T^{5} + 3444505 T^{6} + 22157982 T^{7} + 131487746 T^{8} + 454371856 T^{9} + 2073071593 T^{10} \))(\( 1 - 4 T + 282 T^{2} - 914 T^{3} + 36665 T^{4} - 94644 T^{5} + 2676545 T^{6} - 4870706 T^{7} + 109702794 T^{8} - 113592964 T^{9} + 2073071593 T^{10} \))
$79$ (\( 1 + 26 T + 314 T^{2} + 2054 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 177 T^{2} - 1744 T^{3} + 13983 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 + 14 T + 315 T^{2} + 3176 T^{3} + 45082 T^{4} + 346676 T^{5} + 3561478 T^{6} + 19821416 T^{7} + 155307285 T^{8} + 545301134 T^{9} + 3077056399 T^{10} \))(\( 1 - 4 T + 107 T^{2} + 144 T^{3} + 11770 T^{4} - 28216 T^{5} + 929830 T^{6} + 898704 T^{7} + 52755173 T^{8} - 155800324 T^{9} + 3077056399 T^{10} \))(\( 1 - 28 T + 579 T^{2} - 8320 T^{3} + 100402 T^{4} - 956712 T^{5} + 7931758 T^{6} - 51925120 T^{7} + 285469581 T^{8} - 1090602268 T^{9} + 3077056399 T^{10} \))
$83$ (\( 1 + 49 T^{2} + 6889 T^{4} \))(\( 1 + 18 T + 309 T^{2} + 2852 T^{3} + 25647 T^{4} + 124002 T^{5} + 571787 T^{6} \))(\( 1 + 2 T + 114 T^{2} + 338 T^{3} + 12089 T^{4} + 78912 T^{5} + 1003387 T^{6} + 2328482 T^{7} + 65183718 T^{8} + 94916642 T^{9} + 3939040643 T^{10} \))(\( 1 + 6 T + 326 T^{2} + 1666 T^{3} + 48333 T^{4} + 199160 T^{5} + 4011639 T^{6} + 11477074 T^{7} + 186402562 T^{8} + 284749926 T^{9} + 3939040643 T^{10} \))(\( 1 - 18 T + 418 T^{2} - 4746 T^{3} + 63337 T^{4} - 530832 T^{5} + 5256971 T^{6} - 32695194 T^{7} + 239006966 T^{8} - 854249778 T^{9} + 3939040643 T^{10} \))
$89$ (\( 1 - T + 97 T^{2} - 89 T^{3} + 7921 T^{4} \))(\( 1 + 3 T + 153 T^{2} + 265 T^{3} + 13617 T^{4} + 23763 T^{5} + 704969 T^{6} \))(\( 1 - 6 T + 305 T^{2} - 1284 T^{3} + 45117 T^{4} - 153431 T^{5} + 4015413 T^{6} - 10170564 T^{7} + 215015545 T^{8} - 376453446 T^{9} + 5584059449 T^{10} \))(\( 1 + 20 T + 491 T^{2} + 6302 T^{3} + 87253 T^{4} + 799619 T^{5} + 7765517 T^{6} + 49918142 T^{7} + 346139779 T^{8} + 1254844820 T^{9} + 5584059449 T^{10} \))(\( 1 + 217 T^{2} + 1284 T^{3} + 17623 T^{4} + 224799 T^{5} + 1568447 T^{6} + 10170564 T^{7} + 152978273 T^{8} + 5584059449 T^{10} \))
$97$ (\( 1 + 7 T + 47 T^{2} + 679 T^{3} + 9409 T^{4} \))(\( 1 - 3 T + 231 T^{2} - 349 T^{3} + 22407 T^{4} - 28227 T^{5} + 912673 T^{6} \))(\( 1 - 20 T + 207 T^{2} - 2236 T^{3} + 33747 T^{4} - 423407 T^{5} + 3273459 T^{6} - 21038524 T^{7} + 188923311 T^{8} - 1770585620 T^{9} + 8587340257 T^{10} \))(\( 1 + 24 T + 363 T^{2} + 2360 T^{3} + 3237 T^{4} - 115965 T^{5} + 313989 T^{6} + 22205240 T^{7} + 331300299 T^{8} + 2124702744 T^{9} + 8587340257 T^{10} \))(\( 1 - 4 T + 405 T^{2} - 1326 T^{3} + 71967 T^{4} - 181845 T^{5} + 6980799 T^{6} - 12476334 T^{7} + 369632565 T^{8} - 354117124 T^{9} + 8587340257 T^{10} \))
show more
show less