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
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 | $1$ | $0.216$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(-1\) | $-$ | \(q-2q^{4}-q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\) |