Properties

Label 490.2.a
Level 490
Weight 2
Character orbit a
Rep. character \(\chi_{490}(1,\cdot)\)
Character field \(\Q\)
Dimension 15
Newform subspaces 13
Sturm bound 168
Trace bound 11

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Defining parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(168\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(490))\).

Total New Old
Modular forms 100 15 85
Cusp forms 69 15 54
Eisenstein series 31 0 31

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

\(2\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(5\)
Minus space\(-\)\(10\)

Trace form

\( 15q - q^{2} + 15q^{4} + q^{5} - q^{8} + 23q^{9} + O(q^{10}) \) \( 15q - q^{2} + 15q^{4} + q^{5} - q^{8} + 23q^{9} + q^{10} + 6q^{13} + 4q^{15} + 15q^{16} - 2q^{17} + 3q^{18} + q^{20} - 4q^{22} + 15q^{25} + 6q^{26} - 2q^{29} - 8q^{31} - q^{32} - 2q^{34} + 23q^{36} - 46q^{37} - 48q^{39} + q^{40} - 2q^{41} - 52q^{43} - 3q^{45} + 8q^{46} - 8q^{47} - q^{50} + 32q^{51} + 6q^{52} + 18q^{53} + 4q^{55} - 40q^{57} + 2q^{58} + 8q^{59} + 4q^{60} + 14q^{61} - 8q^{62} + 15q^{64} - 2q^{65} - 36q^{67} - 2q^{68} + 40q^{71} + 3q^{72} - 2q^{73} + 14q^{74} + 24q^{78} - 32q^{79} + q^{80} + 55q^{81} - 2q^{82} - 8q^{83} + 14q^{85} + 16q^{86} - 4q^{88} - 10q^{89} - 3q^{90} - 24q^{93} - 8q^{94} + 4q^{95} - 2q^{97} - 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(490))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7
490.2.a.a \(1\) \(3.913\) \(\Q\) None \(-1\) \(-2\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{8}+\cdots\)
490.2.a.b \(1\) \(3.913\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
490.2.a.c \(1\) \(3.913\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
490.2.a.d \(1\) \(3.913\) \(\Q\) None \(-1\) \(2\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}-q^{8}+\cdots\)
490.2.a.e \(1\) \(3.913\) \(\Q\) None \(1\) \(-3\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}-3q^{3}+q^{4}+q^{5}-3q^{6}+q^{8}+\cdots\)
490.2.a.f \(1\) \(3.913\) \(\Q\) None \(1\) \(-2\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{8}+\cdots\)
490.2.a.g \(1\) \(3.913\) \(\Q\) None \(1\) \(-2\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{8}+\cdots\)
490.2.a.h \(1\) \(3.913\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
490.2.a.i \(1\) \(3.913\) \(\Q\) None \(1\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{8}+\cdots\)
490.2.a.j \(1\) \(3.913\) \(\Q\) None \(1\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{8}+\cdots\)
490.2.a.k \(1\) \(3.913\) \(\Q\) None \(1\) \(3\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+3q^{3}+q^{4}-q^{5}+3q^{6}+q^{8}+\cdots\)
490.2.a.l \(2\) \(3.913\) \(\Q(\sqrt{2}) \) None \(-2\) \(-4\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+(-2+\beta )q^{3}+q^{4}-q^{5}+(2+\cdots)q^{6}+\cdots\)
490.2.a.m \(2\) \(3.913\) \(\Q(\sqrt{2}) \) None \(-2\) \(4\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+(2+\beta )q^{3}+q^{4}+q^{5}+(-2+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(490))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(490)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4} \))(\( 1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4} \))
$5$ (\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))
$7$ 1
$11$ (\( 1 - 3 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} \))
$13$ (\( 1 + T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 4 T + 22 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 22 T^{2} + 52 T^{3} + 169 T^{4} \))
$17$ (\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 8 T + 48 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 136 T^{3} + 289 T^{4} \))
$19$ (\( 1 + T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 4 T + 40 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 40 T^{2} - 76 T^{3} + 361 T^{4} \))
$23$ (\( 1 - 9 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 8 T + 54 T^{2} + 184 T^{3} + 529 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 184 T^{3} + 529 T^{4} \))
$29$ (\( 1 - 6 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 4 T + 54 T^{2} + 116 T^{3} + 841 T^{4} \))(\( 1 + 4 T + 54 T^{2} + 116 T^{3} + 841 T^{4} \))
$31$ (\( 1 - 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 54 T^{2} + 961 T^{4} \))(\( 1 + 54 T^{2} + 961 T^{4} \))
$37$ (\( 1 + 7 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} \))
$41$ (\( 1 - 3 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 + 8 T + 48 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 328 T^{3} + 1681 T^{4} \))
$43$ (\( 1 - 2 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + 12 T + 114 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 + 12 T + 114 T^{2} + 516 T^{3} + 1849 T^{4} \))
$47$ (\( 1 - 9 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 16 T + 150 T^{2} + 752 T^{3} + 2209 T^{4} \))(\( 1 - 16 T + 150 T^{2} - 752 T^{3} + 2209 T^{4} \))
$53$ (\( 1 - 9 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 20 T + 216 T^{2} + 1180 T^{3} + 3481 T^{4} \))(\( 1 - 20 T + 216 T^{2} - 1180 T^{3} + 3481 T^{4} \))
$61$ (\( 1 - 8 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - T + 61 T^{2} \))(\( 1 - 4 T - 2 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 4 T - 2 T^{2} + 244 T^{3} + 3721 T^{4} \))
$67$ (\( 1 - 8 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 8 T + 118 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 118 T^{2} + 536 T^{3} + 4489 T^{4} \))
$71$ (\( 1 + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 16 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} \))(\( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} \))
$73$ (\( 1 + 4 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 16 T + 208 T^{2} - 1168 T^{3} + 5329 T^{4} \))(\( 1 + 16 T + 208 T^{2} + 1168 T^{3} + 5329 T^{4} \))
$79$ (\( 1 + 10 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 8 T + 166 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 166 T^{2} + 632 T^{3} + 6241 T^{4} \))
$83$ (\( 1 + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 7 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 7 T + 83 T^{2} \))(\( 1 + 4 T + 152 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 - 4 T + 152 T^{2} - 332 T^{3} + 6889 T^{4} \))
$89$ (\( 1 - 6 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - T + 89 T^{2} \))(\( 1 + 16 T^{2} + 7921 T^{4} \))(\( 1 + 16 T^{2} + 7921 T^{4} \))
$97$ (\( 1 + 10 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 24 T + 320 T^{2} - 2328 T^{3} + 9409 T^{4} \))(\( 1 + 24 T + 320 T^{2} + 2328 T^{3} + 9409 T^{4} \))
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