Defining parameters
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(9\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(13))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9 | 7 | 2 |
Cusp forms | 7 | 7 | 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.
\(13\) | Dim |
---|---|
\(+\) | \(4\) |
\(-\) | \(3\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(13))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 13 | |||||||
13.8.a.a | $1$ | $4.061$ | \(\Q\) | None | \(10\) | \(-73\) | \(-295\) | \(1373\) | $-$ | \(q+10q^{2}-73q^{3}-28q^{4}-295q^{5}+\cdots\) | |
13.8.a.b | $2$ | $4.061$ | \(\Q(\sqrt{337}) \) | None | \(-19\) | \(45\) | \(-353\) | \(-2009\) | $-$ | \(q+(-9-\beta )q^{2}+(21+3\beta )q^{3}+(37+19\beta )q^{4}+\cdots\) | |
13.8.a.c | $4$ | $4.061$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(15\) | \(80\) | \(258\) | \(1692\) | $+$ | \(q+(4-\beta _{1})q^{2}+(21-2\beta _{1}+\beta _{2})q^{3}+\cdots\) |