Defining parameters
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(37))\).
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.
\(37\) | Dim |
---|---|
\(+\) | \(5\) |
\(-\) | \(4\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(37))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 37 | |||||||
37.4.a.a | $4$ | $2.183$ | 4.4.21208.1 | None | \(-6\) | \(-11\) | \(-29\) | \(-32\) | $-$ | \(q+(-2+\beta _{2}-\beta _{3})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\) | |
37.4.a.b | $5$ | $2.183$ | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) | None | \(4\) | \(13\) | \(11\) | \(24\) | $+$ | \(q+(1-\beta _{1})q^{2}+(3-\beta _{2})q^{3}+(3-\beta _{1}+\cdots)q^{4}+\cdots\) |