Properties

Label 27.3.b
Level 27
Weight 3
Character orbit b
Rep. character \(\chi_{27}(26,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 2
Sturm bound 9
Trace bound 1

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 9 3 6
Cusp forms 3 3 0
Eisenstein series 6 0 6

Trace form

\( 3q - 6q^{4} - 3q^{7} + O(q^{10}) \) \( 3q - 6q^{4} - 3q^{7} + 18q^{10} - 21q^{13} - 6q^{16} - 21q^{19} + 90q^{22} + 57q^{25} - 102q^{28} - 48q^{31} - 108q^{34} + 87q^{37} - 18q^{40} + 78q^{43} + 72q^{46} + 72q^{49} + 96q^{52} - 90q^{55} - 180q^{58} - 273q^{61} + 246q^{64} - 129q^{67} + 90q^{70} + 33q^{73} + 204q^{76} + 159q^{79} - 360q^{82} + 108q^{85} - 90q^{88} - 87q^{91} + 36q^{94} - 3q^{97} + O(q^{100}) \)

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.b.a \(1\) \(0.736\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-13\) \(q+4q^{4}-13q^{7}-q^{13}+2^{4}q^{16}+11q^{19}+\cdots\)
27.3.b.b \(2\) \(0.736\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(10\) \(q+iq^{2}-5q^{4}-iq^{5}+5q^{7}-iq^{8}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 2 T )( 1 + 2 T ) \))(\( 1 + T^{2} + 16 T^{4} \))
$3$ 1
$5$ (\( ( 1 - 5 T )( 1 + 5 T ) \))(\( 1 - 41 T^{2} + 625 T^{4} \))
$7$ (\( 1 + 13 T + 49 T^{2} \))(\( ( 1 - 5 T + 49 T^{2} )^{2} \))
$11$ (\( ( 1 - 11 T )( 1 + 11 T ) \))(\( 1 - 17 T^{2} + 14641 T^{4} \))
$13$ (\( 1 + T + 169 T^{2} \))(\( ( 1 + 10 T + 169 T^{2} )^{2} \))
$17$ (\( ( 1 - 17 T )( 1 + 17 T ) \))(\( 1 - 254 T^{2} + 83521 T^{4} \))
$19$ (\( 1 - 11 T + 361 T^{2} \))(\( ( 1 + 16 T + 361 T^{2} )^{2} \))
$23$ (\( ( 1 - 23 T )( 1 + 23 T ) \))(\( 1 - 914 T^{2} + 279841 T^{4} \))
$29$ (\( ( 1 - 29 T )( 1 + 29 T ) \))(\( 1 - 782 T^{2} + 707281 T^{4} \))
$31$ (\( 1 + 46 T + 961 T^{2} \))(\( ( 1 + T + 961 T^{2} )^{2} \))
$37$ (\( 1 - 47 T + 1369 T^{2} \))(\( ( 1 - 20 T + 1369 T^{2} )^{2} \))
$41$ (\( ( 1 - 41 T )( 1 + 41 T ) \))(\( 1 + 238 T^{2} + 2825761 T^{4} \))
$43$ (\( 1 + 22 T + 1849 T^{2} \))(\( ( 1 - 50 T + 1849 T^{2} )^{2} \))
$47$ (\( ( 1 - 47 T )( 1 + 47 T ) \))(\( 1 - 4382 T^{2} + 4879681 T^{4} \))
$53$ (\( ( 1 - 53 T )( 1 + 53 T ) \))(\( 1 - 4889 T^{2} + 7890481 T^{4} \))
$59$ (\( ( 1 - 59 T )( 1 + 59 T ) \))(\( 1 - 6062 T^{2} + 12117361 T^{4} \))
$61$ (\( 1 + 121 T + 3721 T^{2} \))(\( ( 1 + 76 T + 3721 T^{2} )^{2} \))
$67$ (\( 1 + 109 T + 4489 T^{2} \))(\( ( 1 + 10 T + 4489 T^{2} )^{2} \))
$71$ (\( ( 1 - 71 T )( 1 + 71 T ) \))(\( 1 - 1982 T^{2} + 25411681 T^{4} \))
$73$ (\( 1 + 97 T + 5329 T^{2} \))(\( ( 1 - 65 T + 5329 T^{2} )^{2} \))
$79$ (\( 1 - 131 T + 6241 T^{2} \))(\( ( 1 - 14 T + 6241 T^{2} )^{2} \))
$83$ (\( ( 1 - 83 T )( 1 + 83 T ) \))(\( 1 - 13769 T^{2} + 47458321 T^{4} \))
$89$ (\( ( 1 - 89 T )( 1 + 89 T ) \))(\( 1 - 7742 T^{2} + 62742241 T^{4} \))
$97$ (\( 1 - 167 T + 9409 T^{2} \))(\( ( 1 + 85 T + 9409 T^{2} )^{2} \))
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