Defining parameters
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.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 \(M_{6}(\Gamma_0(13))\).
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.
\(13\) | Dim |
---|---|
\(+\) | \(2\) |
\(-\) | \(3\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(13))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 13 | |||||||
13.6.a.a | $2$ | $2.085$ | \(\Q(\sqrt{17}) \) | None | \(-5\) | \(-28\) | \(-42\) | \(-36\) | $+$ | \(q+(-2-\beta )q^{2}+(-17+6\beta )q^{3}+(-24+\cdots)q^{4}+\cdots\) | |
13.6.a.b | $3$ | $2.085$ | 3.3.168897.1 | None | \(7\) | \(8\) | \(56\) | \(-60\) | $-$ | \(q+(2+\beta _{1})q^{2}+(3-\beta _{1}-\beta _{2})q^{3}+(40+\cdots)q^{4}+\cdots\) |