Defining parameters
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(667\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4003))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 334 | 334 | 0 |
Cusp forms | 333 | 333 | 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.
\(4003\) | Dim |
---|---|
\(+\) | \(154\) |
\(-\) | \(179\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4003))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 4003 | |||||||
4003.2.a.a | $2$ | $31.964$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(0\) | \(-2\) | $+$ | \(q+\beta q^{2}+\beta q^{3}+\beta q^{5}+2q^{6}-q^{7}+\cdots\) | |
4003.2.a.b | $152$ | $31.964$ | None | \(-22\) | \(-18\) | \(-59\) | \(-19\) | $+$ | |||
4003.2.a.c | $179$ | $31.964$ | None | \(22\) | \(16\) | \(61\) | \(21\) | $-$ |