Defining parameters
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(43))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 34 | 32 | 2 |
Cusp forms | 32 | 32 | 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 |
---|---|
\(+\) | \(15\) |
\(-\) | \(17\) |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(43))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 43 | |||||||
43.10.a.a | $15$ | $22.147$ | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) | None | \(-32\) | \(-317\) | \(-4717\) | \(-9680\) | $+$ | \(q+(-2-\beta _{1})q^{2}+(-21-\beta _{2})q^{3}+(6^{3}+\cdots)q^{4}+\cdots\) | |
43.10.a.b | $17$ | $22.147$ | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) | None | \(48\) | \(169\) | \(4033\) | \(-76\) | $-$ | \(q+(3-\beta _{1})q^{2}+(10-\beta _{3})q^{3}+(267-4\beta _{1}+\cdots)q^{4}+\cdots\) |