Properties

Label 27.2.a
Level 27
Weight 2
Character orbit a
Rep. character \(\chi_{27}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 27.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(27))\).

Total New Old
Modular forms 6 1 5
Cusp forms 1 1 0
Eisenstein series 5 0 5

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

\(3\)Dim.
\(-\)\(1\)

Trace form

\( q - 2q^{4} - q^{7} + O(q^{10}) \) \( q - 2q^{4} - q^{7} + 5q^{13} + 4q^{16} - 7q^{19} - 5q^{25} + 2q^{28} - 4q^{31} + 11q^{37} + 8q^{43} - 6q^{49} - 10q^{52} - q^{61} - 8q^{64} + 5q^{67} - 7q^{73} + 14q^{76} + 17q^{79} - 5q^{91} - 19q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
27.2.a.a \(1\) \(0.216\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-2q^{4}-q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T^{2} \)
$3$ 1
$5$ \( 1 + 5 T^{2} \)
$7$ \( 1 + T + 7 T^{2} \)
$11$ \( 1 + 11 T^{2} \)
$13$ \( 1 - 5 T + 13 T^{2} \)
$17$ \( 1 + 17 T^{2} \)
$19$ \( 1 + 7 T + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 + 29 T^{2} \)
$31$ \( 1 + 4 T + 31 T^{2} \)
$37$ \( 1 - 11 T + 37 T^{2} \)
$41$ \( 1 + 41 T^{2} \)
$43$ \( 1 - 8 T + 43 T^{2} \)
$47$ \( 1 + 47 T^{2} \)
$53$ \( 1 + 53 T^{2} \)
$59$ \( 1 + 59 T^{2} \)
$61$ \( 1 + T + 61 T^{2} \)
$67$ \( 1 - 5 T + 67 T^{2} \)
$71$ \( 1 + 71 T^{2} \)
$73$ \( 1 + 7 T + 73 T^{2} \)
$79$ \( 1 - 17 T + 79 T^{2} \)
$83$ \( 1 + 83 T^{2} \)
$89$ \( 1 + 89 T^{2} \)
$97$ \( 1 + 19 T + 97 T^{2} \)
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