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.
\(2\) | \(3\) | Fricke | Dim. |
---|---|---|---|
\(-\) | \(+\) | \(-\) | \(1\) |
Plus space | \(+\) | \(0\) | |
Minus space | \(-\) | \(1\) |
Trace form
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
\( S_{2}^{\mathrm{old}}(\Gamma_0(108)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 2}\)