Properties

Label 108.2.a
Level 108
Weight 2
Character orbit a
Rep. character \(\chi_{108}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 36
Trace bound 0

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Defining parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 108.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(108))\).

Total New Old
Modular forms 27 1 26
Cusp forms 10 1 9
Eisenstein series 17 0 17

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.
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q + 5q^{7} + O(q^{10}) \) \( q + 5q^{7} - 7q^{13} - q^{19} - 5q^{25} - 4q^{31} - q^{37} + 8q^{43} + 18q^{49} - 13q^{61} + 11q^{67} + 17q^{73} - 13q^{79} - 35q^{91} + 5q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(108))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
108.2.a.a \(1\) \(0.862\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(-\) \(+\) \(q+5q^{7}-7q^{13}-q^{19}-5q^{25}-4q^{31}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(108))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(108)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

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