Defining parameters
Level: | \( N \) | \(=\) | \( 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2003.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(334\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2003))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 168 | 168 | 0 |
Cusp forms | 167 | 167 | 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.
\(2003\) | Dim |
---|---|
\(+\) | \(75\) |
\(-\) | \(92\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2003))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2003 | |||||||
2003.2.a.a | $75$ | $15.994$ | None | \(-7\) | \(-18\) | \(-24\) | \(-38\) | $+$ | |||
2003.2.a.b | $92$ | $15.994$ | None | \(5\) | \(16\) | \(24\) | \(38\) | $-$ |