Defining parameters
Level: | \( N \) | \(=\) | \( 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 463.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(77\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(463))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 39 | 39 | 0 |
Cusp forms | 38 | 38 | 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.
\(463\) | Dim |
---|---|
\(+\) | \(16\) |
\(-\) | \(22\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(463))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 463 | |||||||
463.2.a.a | $16$ | $3.697$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(-9\) | \(-6\) | \(-16\) | \(-10\) | $+$ | \(q+(-1+\beta _{1})q^{2}-\beta _{6}q^{3}+(1-\beta _{1}-\beta _{12}+\cdots)q^{4}+\cdots\) | |
463.2.a.b | $22$ | $3.697$ | None | \(8\) | \(4\) | \(14\) | \(2\) | $-$ |