Defining parameters
Level: | \( N \) | \(=\) | \( 8038 = 2 \cdot 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8038.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(2010\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8038))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1007 | 334 | 673 |
Cusp forms | 1004 | 334 | 670 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(4019\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(84\) |
\(+\) | \(-\) | $-$ | \(83\) |
\(-\) | \(+\) | $-$ | \(92\) |
\(-\) | \(-\) | $+$ | \(75\) |
Plus space | \(+\) | \(159\) | |
Minus space | \(-\) | \(175\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8038))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 4019 | |||||||
8038.2.a.a | $75$ | $64.184$ | None | \(75\) | \(-30\) | \(-29\) | \(-31\) | $-$ | $-$ | |||
8038.2.a.b | $83$ | $64.184$ | None | \(-83\) | \(20\) | \(31\) | \(-3\) | $+$ | $-$ | |||
8038.2.a.c | $84$ | $64.184$ | None | \(-84\) | \(-19\) | \(-32\) | \(1\) | $+$ | $+$ | |||
8038.2.a.d | $92$ | $64.184$ | None | \(92\) | \(31\) | \(28\) | \(29\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8038))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8038)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4019))\)\(^{\oplus 2}\)