Properties

Label 27.3.d
Level 27
Weight 3
Character orbit d
Rep. character \(\chi_{27}(8,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
Newform subspaces 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 27.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(27, [\chi])\).

Total New Old
Modular forms 18 6 12
Cusp forms 6 2 4
Eisenstein series 12 4 8

Trace form

\( 2q + 3q^{2} - q^{4} - 6q^{5} - 2q^{7} + O(q^{10}) \) \( 2q + 3q^{2} - q^{4} - 6q^{5} - 2q^{7} - 12q^{10} + 3q^{11} + 4q^{13} - 6q^{14} + 11q^{16} + 22q^{19} + 6q^{20} + 3q^{22} + 48q^{23} - 13q^{25} + 4q^{28} - 78q^{29} - 32q^{31} - 27q^{32} - 27q^{34} - 68q^{37} + 33q^{38} + 30q^{40} + 21q^{41} + 61q^{43} + 96q^{46} + 84q^{47} + 45q^{49} - 39q^{50} + 4q^{52} - 12q^{55} + 30q^{56} - 78q^{58} - 87q^{59} - 56q^{61} - 142q^{64} - 24q^{65} + 31q^{67} + 27q^{68} + 12q^{70} + 130q^{73} - 102q^{74} - 11q^{76} - 6q^{77} - 38q^{79} + 42q^{82} + 84q^{83} - 54q^{85} + 183q^{86} + 15q^{88} - 16q^{91} - 48q^{92} + 84q^{94} - 66q^{95} + 115q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(27, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
27.3.d.a \(2\) \(0.736\) \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(-6\) \(-2\) \(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+2\zeta_{6})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(27, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 3 T + 7 T^{2} - 12 T^{3} + 16 T^{4} \)
$3$ 1
$5$ \( 1 + 6 T + 37 T^{2} + 150 T^{3} + 625 T^{4} \)
$7$ \( ( 1 - 11 T + 49 T^{2} )( 1 + 13 T + 49 T^{2} ) \)
$11$ \( 1 - 3 T + 124 T^{2} - 363 T^{3} + 14641 T^{4} \)
$13$ \( 1 - 4 T - 153 T^{2} - 676 T^{3} + 28561 T^{4} \)
$17$ \( 1 - 335 T^{2} + 83521 T^{4} \)
$19$ \( ( 1 - 11 T + 361 T^{2} )^{2} \)
$23$ \( 1 - 48 T + 1297 T^{2} - 25392 T^{3} + 279841 T^{4} \)
$29$ \( 1 + 78 T + 2869 T^{2} + 65598 T^{3} + 707281 T^{4} \)
$31$ \( 1 + 32 T + 63 T^{2} + 30752 T^{3} + 923521 T^{4} \)
$37$ \( ( 1 + 34 T + 1369 T^{2} )^{2} \)
$41$ \( 1 - 21 T + 1828 T^{2} - 35301 T^{3} + 2825761 T^{4} \)
$43$ \( ( 1 - 83 T + 1849 T^{2} )( 1 + 22 T + 1849 T^{2} ) \)
$47$ \( 1 - 84 T + 4561 T^{2} - 185556 T^{3} + 4879681 T^{4} \)
$53$ \( ( 1 - 53 T )^{2}( 1 + 53 T )^{2} \)
$59$ \( 1 + 87 T + 6004 T^{2} + 302847 T^{3} + 12117361 T^{4} \)
$61$ \( 1 + 56 T - 585 T^{2} + 208376 T^{3} + 13845841 T^{4} \)
$67$ \( 1 - 31 T - 3528 T^{2} - 139159 T^{3} + 20151121 T^{4} \)
$71$ \( 1 - 9110 T^{2} + 25411681 T^{4} \)
$73$ \( ( 1 - 65 T + 5329 T^{2} )^{2} \)
$79$ \( 1 + 38 T - 4797 T^{2} + 237158 T^{3} + 38950081 T^{4} \)
$83$ \( 1 - 84 T + 9241 T^{2} - 578676 T^{3} + 47458321 T^{4} \)
$89$ \( 1 - 290 T^{2} + 62742241 T^{4} \)
$97$ \( 1 - 115 T + 3816 T^{2} - 1082035 T^{3} + 88529281 T^{4} \)
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