Defining parameters
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(11\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(13))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11 | 9 | 2 |
Cusp forms | 9 | 9 | 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 |
---|---|
\(+\) | \(4\) |
\(-\) | \(5\) |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(13))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 13 | |||||||
13.10.a.a | $4$ | $6.695$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(-33\) | \(-163\) | \(471\) | \(-11241\) | $+$ | \(q+(-8-\beta _{1})q^{2}+(-41+2\beta _{1}-\beta _{3})q^{3}+\cdots\) | |
13.10.a.b | $5$ | $6.695$ | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) | None | \(15\) | \(161\) | \(1803\) | \(10099\) | $-$ | \(q+(3+\beta _{1})q^{2}+(2^{5}+2\beta _{1}-\beta _{2})q^{3}+\cdots\) |