Properties

Label 18.3.b
Level 18
Weight 3
Character orbit b
Rep. character \(\chi_{18}(17,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 18.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(18, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

Trace form

\( 2q - 4q^{4} - 8q^{7} + O(q^{10}) \) \( 2q - 4q^{4} - 8q^{7} + 12q^{10} + 16q^{13} + 8q^{16} - 32q^{19} - 48q^{22} + 14q^{25} + 16q^{28} + 88q^{31} + 36q^{34} - 68q^{37} - 24q^{40} - 80q^{43} + 48q^{46} - 66q^{49} - 32q^{52} + 144q^{55} - 12q^{58} + 100q^{61} - 16q^{64} + 16q^{67} - 48q^{70} - 32q^{73} + 64q^{76} - 152q^{79} - 132q^{82} - 108q^{85} + 96q^{88} - 64q^{91} + 240q^{94} + 352q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
18.3.b.a \(2\) \(0.490\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T^{2} \)
$3$ 1
$5$ \( 1 - 32 T^{2} + 625 T^{4} \)
$7$ \( ( 1 + 4 T + 49 T^{2} )^{2} \)
$11$ \( ( 1 - 14 T + 121 T^{2} )( 1 + 14 T + 121 T^{2} ) \)
$13$ \( ( 1 - 8 T + 169 T^{2} )^{2} \)
$17$ \( 1 - 416 T^{2} + 83521 T^{4} \)
$19$ \( ( 1 + 16 T + 361 T^{2} )^{2} \)
$23$ \( 1 - 770 T^{2} + 279841 T^{4} \)
$29$ \( 1 - 1664 T^{2} + 707281 T^{4} \)
$31$ \( ( 1 - 44 T + 961 T^{2} )^{2} \)
$37$ \( ( 1 + 34 T + 1369 T^{2} )^{2} \)
$41$ \( 1 - 1184 T^{2} + 2825761 T^{4} \)
$43$ \( ( 1 + 40 T + 1849 T^{2} )^{2} \)
$47$ \( 1 + 2782 T^{2} + 4879681 T^{4} \)
$53$ \( 1 - 4160 T^{2} + 7890481 T^{4} \)
$59$ \( 1 - 5810 T^{2} + 12117361 T^{4} \)
$61$ \( ( 1 - 50 T + 3721 T^{2} )^{2} \)
$67$ \( ( 1 - 8 T + 4489 T^{2} )^{2} \)
$71$ \( 1 - 7490 T^{2} + 25411681 T^{4} \)
$73$ \( ( 1 + 16 T + 5329 T^{2} )^{2} \)
$79$ \( ( 1 + 76 T + 6241 T^{2} )^{2} \)
$83$ \( 1 + 334 T^{2} + 47458321 T^{4} \)
$89$ \( 1 - 15680 T^{2} + 62742241 T^{4} \)
$97$ \( ( 1 - 176 T + 9409 T^{2} )^{2} \)
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