Defining parameters
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(2007\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8026))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1005 | 334 | 671 |
Cusp forms | 1002 | 334 | 668 |
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.
\(2\) | \(4013\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(81\) |
\(+\) | \(-\) | $-$ | \(86\) |
\(-\) | \(+\) | $-$ | \(96\) |
\(-\) | \(-\) | $+$ | \(71\) |
Plus space | \(+\) | \(152\) | |
Minus space | \(-\) | \(182\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8026))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 4013 | |||||||
8026.2.a.a | $71$ | $64.088$ | None | \(71\) | \(-9\) | \(-34\) | \(-19\) | $-$ | $-$ | |||
8026.2.a.b | $81$ | $64.088$ | None | \(-81\) | \(-10\) | \(-26\) | \(3\) | $+$ | $+$ | |||
8026.2.a.c | $86$ | $64.088$ | None | \(-86\) | \(11\) | \(25\) | \(-3\) | $+$ | $-$ | |||
8026.2.a.d | $96$ | $64.088$ | None | \(96\) | \(8\) | \(39\) | \(19\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8026))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8026)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4013))\)\(^{\oplus 2}\)