Defining parameters
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(7\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(5))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7 | 5 | 2 |
Cusp forms | 5 | 5 | 0 |
Eisenstein series | 2 | 0 | 2 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | Dim |
---|---|
\(+\) | \(2\) |
\(-\) | \(3\) |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | |||||||
5.14.a.a | $2$ | $5.362$ | \(\Q(\sqrt{499}) \) | None | \(-80\) | \(780\) | \(-31250\) | \(-616300\) | $+$ | \(q+(-40+\beta )q^{2}+(390-12\beta )q^{3}+(1392+\cdots)q^{4}+\cdots\) | |
5.14.a.b | $3$ | $5.362$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(142\) | \(416\) | \(46875\) | \(448292\) | $-$ | \(q+(47-\beta _{1})q^{2}+(138-3\beta _{1}-\beta _{2})q^{3}+\cdots\) |