Defining parameters
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(91\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(547))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 46 | 46 | 0 |
Cusp forms | 45 | 45 | 0 |
Eisenstein series | 1 | 1 | 0 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(547\) | Dim |
---|---|
\(+\) | \(20\) |
\(-\) | \(25\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(547))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 547 | |||||||
547.2.a.a | $2$ | $4.368$ | \(\Q(\sqrt{2}) \) | None | \(-2\) | \(0\) | \(0\) | \(4\) | $+$ | \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots\) | |
547.2.a.b | $18$ | $4.368$ | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) | None | \(-4\) | \(-10\) | \(-27\) | \(-11\) | $+$ | \(q-\beta _{1}q^{2}+(-1+\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\) | |
547.2.a.c | $25$ | $4.368$ | None | \(4\) | \(8\) | \(29\) | \(5\) | $-$ |