Properties

Label 18.8.a
Level 18
Weight 8
Character orbit a
Rep. character \(\chi_{18}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 2
Sturm bound 24
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 18.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(18))\).

Total New Old
Modular forms 25 2 23
Cusp forms 17 2 15
Eisenstein series 8 0 8

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

\(2\)\(3\)FrickeDim.
\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(1\)

Trace form

\( 2q + 128q^{4} + 324q^{5} - 560q^{7} + O(q^{10}) \) \( 2q + 128q^{4} + 324q^{5} - 560q^{7} + 768q^{10} - 8424q^{11} - 2420q^{13} + 20736q^{14} + 8192q^{16} - 8100q^{17} - 15080q^{19} + 20736q^{20} + 49920q^{22} - 110160q^{23} - 99154q^{25} + 41472q^{26} - 35840q^{28} + 144180q^{29} + 260704q^{31} - 170496q^{34} + 33696q^{35} + 124060q^{37} - 518400q^{38} + 49152q^{40} + 628236q^{41} - 787160q^{43} - 539136q^{44} - 218112q^{46} - 38880q^{47} + 1868946q^{49} + 248832q^{50} - 154880q^{52} + 707940q^{53} - 1065168q^{55} + 1327104q^{56} + 487680q^{58} - 3385800q^{59} - 832916q^{61} + 1555200q^{62} + 524288q^{64} - 143208q^{65} - 3416840q^{67} - 518400q^{68} + 3144192q^{70} - 4301424q^{71} + 3640180q^{73} + 1575936q^{74} - 965120q^{76} + 10445760q^{77} + 240640q^{79} + 1327104q^{80} - 5199360q^{82} - 7902360q^{83} - 2335176q^{85} - 3794688q^{86} + 3194880q^{88} + 5959980q^{89} + 7396064q^{91} - 7050240q^{92} - 7251456q^{94} - 5553360q^{95} + 4622020q^{97} - 11612160q^{98} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(18))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
18.8.a.a \(1\) \(5.623\) \(\Q\) None \(-8\) \(0\) \(114\) \(-1576\) \(+\) \(-\) \(q-8q^{2}+2^{6}q^{4}+114q^{5}-1576q^{7}+\cdots\)
18.8.a.b \(1\) \(5.623\) \(\Q\) None \(8\) \(0\) \(210\) \(1016\) \(-\) \(-\) \(q+8q^{2}+2^{6}q^{4}+210q^{5}+1016q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 8 T \))(\( 1 - 8 T \))
$3$ 1
$5$ (\( 1 - 114 T + 78125 T^{2} \))(\( 1 - 210 T + 78125 T^{2} \))
$7$ (\( 1 + 1576 T + 823543 T^{2} \))(\( 1 - 1016 T + 823543 T^{2} \))
$11$ (\( 1 + 7332 T + 19487171 T^{2} \))(\( 1 + 1092 T + 19487171 T^{2} \))
$13$ (\( 1 + 3802 T + 62748517 T^{2} \))(\( 1 - 1382 T + 62748517 T^{2} \))
$17$ (\( 1 - 6606 T + 410338673 T^{2} \))(\( 1 + 14706 T + 410338673 T^{2} \))
$19$ (\( 1 - 24860 T + 893871739 T^{2} \))(\( 1 + 39940 T + 893871739 T^{2} \))
$23$ (\( 1 + 41448 T + 3404825447 T^{2} \))(\( 1 + 68712 T + 3404825447 T^{2} \))
$29$ (\( 1 - 41610 T + 17249876309 T^{2} \))(\( 1 - 102570 T + 17249876309 T^{2} \))
$31$ (\( 1 - 33152 T + 27512614111 T^{2} \))(\( 1 - 227552 T + 27512614111 T^{2} \))
$37$ (\( 1 + 36466 T + 94931877133 T^{2} \))(\( 1 - 160526 T + 94931877133 T^{2} \))
$41$ (\( 1 - 639078 T + 194754273881 T^{2} \))(\( 1 + 10842 T + 194754273881 T^{2} \))
$43$ (\( 1 + 156412 T + 271818611107 T^{2} \))(\( 1 + 630748 T + 271818611107 T^{2} \))
$47$ (\( 1 - 433776 T + 506623120463 T^{2} \))(\( 1 + 472656 T + 506623120463 T^{2} \))
$53$ (\( 1 + 786078 T + 1174711139837 T^{2} \))(\( 1 - 1494018 T + 1174711139837 T^{2} \))
$59$ (\( 1 + 745140 T + 2488651484819 T^{2} \))(\( 1 + 2640660 T + 2488651484819 T^{2} \))
$61$ (\( 1 + 1660618 T + 3142742836021 T^{2} \))(\( 1 - 827702 T + 3142742836021 T^{2} \))
$67$ (\( 1 + 3290836 T + 6060711605323 T^{2} \))(\( 1 + 126004 T + 6060711605323 T^{2} \))
$71$ (\( 1 + 5716152 T + 9095120158391 T^{2} \))(\( 1 - 1414728 T + 9095120158391 T^{2} \))
$73$ (\( 1 - 2659898 T + 11047398519097 T^{2} \))(\( 1 - 980282 T + 11047398519097 T^{2} \))
$79$ (\( 1 - 3807440 T + 19203908986159 T^{2} \))(\( 1 + 3566800 T + 19203908986159 T^{2} \))
$83$ (\( 1 + 2229468 T + 27136050989627 T^{2} \))(\( 1 + 5672892 T + 27136050989627 T^{2} \))
$89$ (\( 1 + 5991210 T + 44231334895529 T^{2} \))(\( 1 - 11951190 T + 44231334895529 T^{2} \))
$97$ (\( 1 + 4060126 T + 80798284478113 T^{2} \))(\( 1 - 8682146 T + 80798284478113 T^{2} \))
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