Defining parameters
Level: | \( N \) | \(=\) | \( 6007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6007.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(1001\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6007))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 501 | 501 | 0 |
Cusp forms | 500 | 500 | 0 |
Eisenstein series | 1 | 1 | 0 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(6007\) | Dim |
---|---|
\(+\) | \(237\) |
\(-\) | \(263\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6007))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 6007 | |||||||
6007.2.a.a | $2$ | $47.966$ | \(\Q(\sqrt{5}) \) | None | \(-1\) | \(-3\) | \(1\) | \(-6\) | $-$ | \(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\) | |
6007.2.a.b | $237$ | $47.966$ | None | \(-26\) | \(-24\) | \(-67\) | \(-37\) | $+$ | |||
6007.2.a.c | $261$ | $47.966$ | None | \(26\) | \(25\) | \(66\) | \(37\) | $-$ |