Properties

Label 2100.2.bc
Level 2100
Weight 2
Character orbit bc
Rep. character \(\chi_{2100}(949,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 48
Newform subspaces 8
Sturm bound 960
Trace bound 19

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(960\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2100, [\chi])\).

Total New Old
Modular forms 1032 48 984
Cusp forms 888 48 840
Eisenstein series 144 0 144

Trace form

\( 48q + 24q^{9} + O(q^{10}) \) \( 48q + 24q^{9} + 12q^{11} - 18q^{19} - 2q^{21} - 32q^{29} - 16q^{31} - 2q^{39} - 72q^{41} - 6q^{49} - 8q^{51} + 40q^{59} + 46q^{61} + 16q^{69} + 80q^{71} + 40q^{79} - 24q^{81} + 32q^{89} + 2q^{91} + 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2100.2.bc.a \(4\) \(16.769\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(-3\zeta_{12}+\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2100.2.bc.b \(4\) \(16.769\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2100.2.bc.c \(4\) \(16.769\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+(-\zeta_{12}+3\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2100.2.bc.d \(4\) \(16.769\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+(\zeta_{12}+2\zeta_{12}^{3})q^{7}+\cdots\)
2100.2.bc.e \(8\) \(16.769\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{1}q^{7}-\beta _{3}q^{9}+(-1-\beta _{3}+\cdots)q^{11}+\cdots\)
2100.2.bc.f \(8\) \(16.769\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{3}+(-\zeta_{24}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
2100.2.bc.g \(8\) \(16.769\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{3}+(\zeta_{24}-\zeta_{24}^{5}+\zeta_{24}^{6})q^{7}+\cdots\)
2100.2.bc.h \(8\) \(16.769\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}-\beta _{6}q^{7}-\beta _{3}q^{9}+(3+3\beta _{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 - T^{2} + T^{4} \))(\( 1 - T^{2} + T^{4} \))(\( 1 - T^{2} + T^{4} \))(\( 1 - T^{2} + T^{4} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))
$5$ 1
$7$ (\( 1 - 13 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 + 11 T^{2} + 49 T^{4} \))(\( 1 + 11 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} + 49 T^{4} )^{2} \))(\( 1 + 10 T^{2} + 51 T^{4} + 490 T^{6} + 2401 T^{8} \))(\( 1 + 10 T^{2} + 51 T^{4} + 490 T^{6} + 2401 T^{8} \))(\( ( 1 - 7 T^{2} + 49 T^{4} )^{2} \))
$11$ (\( ( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 + 2 T - 12 T^{2} - 12 T^{3} + 91 T^{4} - 132 T^{5} - 1452 T^{6} + 2662 T^{7} + 14641 T^{8} )^{2} \))(\( ( 1 - 4 T^{2} - 105 T^{4} - 484 T^{6} + 14641 T^{8} )^{2} \))(\( ( 1 - 4 T^{2} - 105 T^{4} - 484 T^{6} + 14641 T^{8} )^{2} \))(\( ( 1 - 6 T + 12 T^{2} - 12 T^{3} + 59 T^{4} - 132 T^{5} + 1452 T^{6} - 7986 T^{7} + 14641 T^{8} )^{2} \))
$13$ (\( ( 1 - 17 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 22 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 25 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + 23 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 19 T^{2} + 169 T^{4} )^{4} \))(\( ( 1 - 14 T^{2} + 315 T^{4} - 2366 T^{6} + 28561 T^{8} )^{2} \))(\( ( 1 - T^{2} + 169 T^{4} )^{4} \))(\( ( 1 - 25 T^{2} + 169 T^{4} )^{4} \))
$17$ (\( ( 1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4} )( 1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4} ) \))(\( ( 1 - 8 T + 47 T^{2} - 136 T^{3} + 289 T^{4} )( 1 + 8 T + 47 T^{2} + 136 T^{3} + 289 T^{4} ) \))(\( 1 + 18 T^{2} + 35 T^{4} + 5202 T^{6} + 83521 T^{8} \))(\( 1 - 2 T^{2} - 285 T^{4} - 578 T^{6} + 83521 T^{8} \))(\( 1 + 52 T^{2} + 1478 T^{4} + 33696 T^{6} + 638099 T^{8} + 9738144 T^{10} + 123444038 T^{12} + 1255153588 T^{14} + 6975757441 T^{16} \))(\( ( 1 + 16 T^{2} - 33 T^{4} + 4624 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 + 16 T^{2} - 33 T^{4} + 4624 T^{6} + 83521 T^{8} )^{2} \))(\( 1 + 52 T^{2} + 1478 T^{4} + 33696 T^{6} + 638099 T^{8} + 9738144 T^{10} + 123444038 T^{12} + 1255153588 T^{14} + 6975757441 T^{16} \))
$19$ (\( ( 1 - 7 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 7 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 - 3 T - 10 T^{2} - 57 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} + 114 T^{3} - 684 T^{4} + 2166 T^{5} + 6137 T^{6} - 41154 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 - T + 19 T^{2} )^{4}( 1 + 8 T + 19 T^{2} )^{4} \))(\( ( 1 + 2 T - 17 T^{2} - 34 T^{3} + 4 T^{4} - 646 T^{5} - 6137 T^{6} + 13718 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 + 4 T - 19 T^{2} - 12 T^{3} + 560 T^{4} - 228 T^{5} - 6859 T^{6} + 27436 T^{7} + 130321 T^{8} )^{2} \))
$23$ (\( 1 - 18 T^{2} - 205 T^{4} - 9522 T^{6} + 279841 T^{8} \))(\( 1 - 18 T^{2} - 205 T^{4} - 9522 T^{6} + 279841 T^{8} \))(\( 1 + 30 T^{2} + 371 T^{4} + 15870 T^{6} + 279841 T^{8} \))(\( 1 + 42 T^{2} + 1235 T^{4} + 22218 T^{6} + 279841 T^{8} \))(\( 1 + 76 T^{2} + 3302 T^{4} + 107616 T^{6} + 2785331 T^{8} + 56928864 T^{10} + 924034982 T^{12} + 11250727564 T^{14} + 78310985281 T^{16} \))(\( ( 1 + 28 T^{2} + 255 T^{4} + 14812 T^{6} + 279841 T^{8} )^{2} \))(\( ( 1 + 10 T^{2} - 429 T^{4} + 5290 T^{6} + 279841 T^{8} )^{2} \))(\( ( 1 + 42 T^{2} + 1235 T^{4} + 22218 T^{6} + 279841 T^{8} )^{2} \))
$29$ (\( ( 1 + 4 T + 29 T^{2} )^{4} \))(\( ( 1 + 4 T + 29 T^{2} )^{4} \))(\( ( 1 + 29 T^{2} )^{4} \))(\( ( 1 - 2 T + 29 T^{2} )^{4} \))(\( ( 1 + 10 T + 76 T^{2} + 290 T^{3} + 841 T^{4} )^{4} \))(\( ( 1 - 12 T + 76 T^{2} - 348 T^{3} + 841 T^{4} )^{4} \))(\( ( 1 - 14 T^{2} + 841 T^{4} )^{4} \))(\( ( 1 + 4 T + 34 T^{2} + 116 T^{3} + 841 T^{4} )^{4} \))
$31$ (\( ( 1 + 3 T - 22 T^{2} + 93 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 3 T - 22 T^{2} + 93 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 5 T - 6 T^{2} - 155 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2}( 1 + 11 T + 31 T^{2} )^{2} \))(\( ( 1 + 2 T - 31 T^{2} - 54 T^{3} + 140 T^{4} - 1674 T^{5} - 29791 T^{6} + 59582 T^{7} + 923521 T^{8} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} + 142 T^{3} - 1004 T^{4} + 4402 T^{5} + 12493 T^{6} - 59582 T^{7} + 923521 T^{8} )^{2} \))(\( ( 1 - 11 T + 31 T^{2} )^{4}( 1 + 7 T + 31 T^{2} )^{4} \))(\( ( 1 - 7 T + 31 T^{2} )^{4}( 1 + 11 T + 31 T^{2} )^{4} \))
$37$ (\( ( 1 + 26 T^{2} + 1369 T^{4} )( 1 + 47 T^{2} + 1369 T^{4} ) \))(\( 1 - 7 T^{2} - 1320 T^{4} - 9583 T^{6} + 1874161 T^{8} \))(\( 1 + 49 T^{2} + 1032 T^{4} + 67081 T^{6} + 1874161 T^{8} \))(\( 1 + 25 T^{2} - 744 T^{4} + 34225 T^{6} + 1874161 T^{8} \))(\( 1 + 126 T^{2} + 9281 T^{4} + 485982 T^{6} + 19885620 T^{8} + 665309358 T^{10} + 17394088241 T^{12} + 323281527534 T^{14} + 3512479453921 T^{16} \))(\( 1 + 110 T^{2} + 6409 T^{4} + 324830 T^{6} + 13948420 T^{8} + 444692270 T^{10} + 12011497849 T^{12} + 282229904990 T^{14} + 3512479453921 T^{16} \))(\( ( 1 + 49 T^{2} + 1032 T^{4} + 67081 T^{6} + 1874161 T^{8} )^{2} \))(\( 1 + 74 T^{2} + 2377 T^{4} + 26714 T^{6} + 232996 T^{8} + 36571466 T^{10} + 4454880697 T^{12} + 189863754266 T^{14} + 3512479453921 T^{16} \))
$41$ (\( ( 1 - 6 T + 41 T^{2} )^{4} \))(\( ( 1 - 6 T + 41 T^{2} )^{4} \))(\( ( 1 - 2 T + 41 T^{2} )^{4} \))(\( ( 1 + 8 T + 41 T^{2} )^{4} \))(\( ( 1 + 6 T + 28 T^{2} + 246 T^{3} + 1681 T^{4} )^{4} \))(\( ( 1 + 64 T^{2} + 1681 T^{4} )^{4} \))(\( ( 1 + 12 T + 100 T^{2} + 492 T^{3} + 1681 T^{4} )^{4} \))(\( ( 1 + 6 T + 84 T^{2} + 246 T^{3} + 1681 T^{4} )^{4} \))
$43$ (\( ( 1 + 35 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 85 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 5 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 61 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 38 T^{2} + 3051 T^{4} - 70262 T^{6} + 3418801 T^{8} )^{2} \))(\( ( 1 - 134 T^{2} + 8115 T^{4} - 247766 T^{6} + 3418801 T^{8} )^{2} \))(\( ( 1 + 4 T^{2} - 906 T^{4} + 7396 T^{6} + 3418801 T^{8} )^{2} \))(\( ( 1 - 108 T^{2} + 6166 T^{4} - 199692 T^{6} + 3418801 T^{8} )^{2} \))
$47$ (\( 1 + 58 T^{2} + 1155 T^{4} + 128122 T^{6} + 4879681 T^{8} \))(\( 1 + 58 T^{2} + 1155 T^{4} + 128122 T^{6} + 4879681 T^{8} \))(\( 1 + 90 T^{2} + 5891 T^{4} + 198810 T^{6} + 4879681 T^{8} \))(\( 1 - 6 T^{2} - 2173 T^{4} - 13254 T^{6} + 4879681 T^{8} \))(\( ( 1 + 58 T^{2} + 1155 T^{4} + 128122 T^{6} + 4879681 T^{8} )^{2} \))(\( ( 1 + 58 T^{2} + 1155 T^{4} + 128122 T^{6} + 4879681 T^{8} )^{2} \))(\( 1 + 80 T^{2} + 2974 T^{4} - 79360 T^{6} - 7279805 T^{8} - 175306240 T^{10} + 14512171294 T^{12} + 862337226320 T^{14} + 23811286661761 T^{16} \))(\( 1 + 12 T^{2} + 1990 T^{4} - 75168 T^{6} - 1790061 T^{8} - 166046112 T^{10} + 9710565190 T^{12} + 129350583948 T^{14} + 23811286661761 T^{16} \))
$53$ (\( 1 - 38 T^{2} - 1365 T^{4} - 106742 T^{6} + 7890481 T^{8} \))(\( 1 + 102 T^{2} + 7595 T^{4} + 286518 T^{6} + 7890481 T^{8} \))(\( 1 - 38 T^{2} - 1365 T^{4} - 106742 T^{6} + 7890481 T^{8} \))(\( 1 + 42 T^{2} - 1045 T^{4} + 117978 T^{6} + 7890481 T^{8} \))(\( 1 + 148 T^{2} + 11258 T^{4} + 744144 T^{6} + 43918499 T^{8} + 2090300496 T^{10} + 88831035098 T^{12} + 3280325447092 T^{14} + 62259690411361 T^{16} \))(\( ( 1 + 34 T^{2} - 1653 T^{4} + 95506 T^{6} + 7890481 T^{8} )^{2} \))(\( ( 1 + 88 T^{2} + 4935 T^{4} + 247192 T^{6} + 7890481 T^{8} )^{2} \))(\( 1 + 148 T^{2} + 11510 T^{4} + 706848 T^{6} + 38616419 T^{8} + 1985536032 T^{10} + 90819436310 T^{12} + 3280325447092 T^{14} + 62259690411361 T^{16} \))
$59$ (\( ( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 8 T + 5 T^{2} + 472 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} - 590 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 6 T - 28 T^{2} + 324 T^{3} - 1509 T^{4} + 19116 T^{5} - 97468 T^{6} - 1232274 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 + 12 T + 8 T^{2} + 216 T^{3} + 6519 T^{4} + 12744 T^{5} + 27848 T^{6} + 2464548 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 12 T + 8 T^{2} - 216 T^{3} + 6519 T^{4} - 12744 T^{5} + 27848 T^{6} - 2464548 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 14 T + 92 T^{2} + 196 T^{3} - 4229 T^{4} + 11564 T^{5} + 320252 T^{6} - 2875306 T^{7} + 12117361 T^{8} )^{2} \))
$61$ (\( ( 1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )^{2}( 1 + 13 T + 61 T^{2} )^{2} \))(\( ( 1 - 13 T + 61 T^{2} )^{2}( 1 - T + 61 T^{2} )^{2} \))(\( ( 1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} )^{4} \))(\( ( 1 - 8 T - 2 T^{2} + 448 T^{3} - 3269 T^{4} + 27328 T^{5} - 7442 T^{6} - 1815848 T^{7} + 13845841 T^{8} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )^{4}( 1 + 13 T + 61 T^{2} )^{4} \))(\( ( 1 - 2 T - 7 T^{2} + 222 T^{3} - 3844 T^{4} + 13542 T^{5} - 26047 T^{6} - 453962 T^{7} + 13845841 T^{8} )^{2} \))
$67$ (\( 1 - 35 T^{2} - 3264 T^{4} - 157115 T^{6} + 20151121 T^{8} \))(\( 1 - 10 T^{2} - 4389 T^{4} - 44890 T^{6} + 20151121 T^{8} \))(\( 1 + 53 T^{2} - 1680 T^{4} + 237917 T^{6} + 20151121 T^{8} \))(\( 1 + 125 T^{2} + 11136 T^{4} + 561125 T^{6} + 20151121 T^{8} \))(\( 1 + 246 T^{2} + 36521 T^{4} + 3694182 T^{6} + 283952580 T^{8} + 16583182998 T^{10} + 735939090041 T^{12} + 22252762013574 T^{14} + 406067677556641 T^{16} \))(\( 1 + 230 T^{2} + 30769 T^{4} + 3025190 T^{6} + 232161940 T^{8} + 13580077910 T^{10} + 620029842049 T^{12} + 20805427898870 T^{14} + 406067677556641 T^{16} \))(\( 1 - 58 T^{2} - 5807 T^{4} - 11194 T^{6} + 48855124 T^{8} - 50249866 T^{10} - 117017559647 T^{12} - 5246586165802 T^{14} + 406067677556641 T^{16} \))(\( ( 1 + 71 T^{2} + 552 T^{4} + 318719 T^{6} + 20151121 T^{8} )^{2} \))
$71$ (\( ( 1 + 10 T + 71 T^{2} )^{4} \))(\( ( 1 - 10 T + 71 T^{2} )^{4} \))(\( ( 1 - 2 T + 71 T^{2} )^{4} \))(\( ( 1 + 71 T^{2} )^{4} \))(\( ( 1 - 22 T + 256 T^{2} - 1562 T^{3} + 5041 T^{4} )^{4} \))(\( ( 1 - 20 T^{2} + 5041 T^{4} )^{4} \))(\( ( 1 + 70 T^{2} + 5041 T^{4} )^{4} \))(\( ( 1 + 4 T + 118 T^{2} + 284 T^{3} + 5041 T^{4} )^{4} \))
$73$ (\( 1 + 25 T^{2} - 4704 T^{4} + 133225 T^{6} + 28398241 T^{8} \))(\( 1 + 145 T^{2} + 15696 T^{4} + 772705 T^{6} + 28398241 T^{8} \))(\( 1 + 145 T^{2} + 15696 T^{4} + 772705 T^{6} + 28398241 T^{8} \))(\( 1 - 79 T^{2} + 912 T^{4} - 420991 T^{6} + 28398241 T^{8} \))(\( ( 1 - 29 T^{2} - 4488 T^{4} - 154541 T^{6} + 28398241 T^{8} )^{2} \))(\( 1 + 206 T^{2} + 22969 T^{4} + 1814654 T^{6} + 124424404 T^{8} + 9670291166 T^{10} + 652279197529 T^{12} + 31174850615534 T^{14} + 806460091894081 T^{16} \))(\( 1 + 98 T^{2} + 3745 T^{4} - 470302 T^{6} - 45250076 T^{8} - 2506239358 T^{10} + 106351412545 T^{12} + 14830754176322 T^{14} + 806460091894081 T^{16} \))(\( 1 + 234 T^{2} + 30521 T^{4} + 3177018 T^{6} + 267142260 T^{8} + 16930328922 T^{10} + 866742713561 T^{12} + 35412208951626 T^{14} + 806460091894081 T^{16} \))
$79$ (\( ( 1 + 3 T - 70 T^{2} + 237 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 7 T - 30 T^{2} - 553 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 3 T - 70 T^{2} + 237 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 6 T - 103 T^{2} - 114 T^{3} + 10236 T^{4} - 9006 T^{5} - 642823 T^{6} + 2958234 T^{7} + 38950081 T^{8} )^{2} \))(\( ( 1 - 11 T + 42 T^{2} - 869 T^{3} + 6241 T^{4} )^{4} \))(\( ( 1 - 10 T - 65 T^{2} - 70 T^{3} + 13084 T^{4} - 5530 T^{5} - 405665 T^{6} - 4930390 T^{7} + 38950081 T^{8} )^{2} \))(\( ( 1 + 8 T - 103 T^{2} + 72 T^{3} + 16592 T^{4} + 5688 T^{5} - 642823 T^{6} + 3944312 T^{7} + 38950081 T^{8} )^{2} \))
$83$ (\( ( 1 - 162 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 158 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 158 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 102 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 188 T^{2} + 20346 T^{4} - 1295132 T^{6} + 47458321 T^{8} )^{2} \))(\( ( 1 - 224 T^{2} + 23730 T^{4} - 1543136 T^{6} + 47458321 T^{8} )^{2} \))(\( ( 1 - 224 T^{2} + 23730 T^{4} - 1543136 T^{6} + 47458321 T^{8} )^{2} \))(\( ( 1 - 316 T^{2} + 38714 T^{4} - 2176924 T^{6} + 47458321 T^{8} )^{2} \))
$89$ (\( ( 1 - 89 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 10 T + 11 T^{2} - 890 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 4 T - 73 T^{2} + 356 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 2 T - 85 T^{2} - 178 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 2 T - 348 T^{3} - 8261 T^{4} - 30972 T^{5} + 1409938 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 12 T - 52 T^{2} + 216 T^{3} + 17679 T^{4} + 19224 T^{5} - 411892 T^{6} + 8459628 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 - 24 T + 272 T^{2} - 3024 T^{3} + 33231 T^{4} - 269136 T^{5} + 2154512 T^{6} - 16919256 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 2 T - 112 T^{2} - 124 T^{3} + 5179 T^{4} - 11036 T^{5} - 887152 T^{6} + 1409938 T^{7} + 62742241 T^{8} )^{2} \))
$97$ (\( ( 1 - 94 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 169 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 94 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 94 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )^{4}( 1 + 18 T + 97 T^{2} )^{4} \))(\( ( 1 - 116 T^{2} + 3750 T^{4} - 1091444 T^{6} + 88529281 T^{8} )^{2} \))(\( ( 1 + 190 T^{2} + 26691 T^{4} + 1787710 T^{6} + 88529281 T^{8} )^{2} \))(\( ( 1 - 170 T^{2} + 16971 T^{4} - 1599530 T^{6} + 88529281 T^{8} )^{2} \))
show more
show less