Defining parameters
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(22\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(43))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 18 | 2 |
Cusp forms | 18 | 18 | 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.
\(43\) | Dim |
---|---|
\(+\) | \(8\) |
\(-\) | \(10\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(43))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 43 | |||||||
43.6.a.a | $8$ | $6.897$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(-12\) | \(-26\) | \(-212\) | \(-136\) | $+$ | \(q+(-2+\beta _{1})q^{2}+(-2-\beta _{1}+\beta _{4}-\beta _{7})q^{3}+\cdots\) | |
43.6.a.b | $10$ | $6.897$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(8\) | \(28\) | \(138\) | \(60\) | $-$ | \(q+(1-\beta _{1})q^{2}+(3+\beta _{6})q^{3}+(21-\beta _{1}+\cdots)q^{4}+\cdots\) |