Defining parameters
Level: | \( N \) | \(=\) | \( 8049 = 3 \cdot 2683 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8049.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(1789\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8049))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 896 | 447 | 449 |
Cusp forms | 893 | 447 | 446 |
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.
\(3\) | \(2683\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(104\) |
\(+\) | \(-\) | $-$ | \(119\) |
\(-\) | \(+\) | $-$ | \(129\) |
\(-\) | \(-\) | $+$ | \(95\) |
Plus space | \(+\) | \(199\) | |
Minus space | \(-\) | \(248\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8049))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 2683 | |||||||
8049.2.a.a | $95$ | $64.272$ | None | \(-9\) | \(95\) | \(-15\) | \(-36\) | $-$ | $-$ | |||
8049.2.a.b | $104$ | $64.272$ | None | \(-9\) | \(-104\) | \(-15\) | \(-10\) | $+$ | $+$ | |||
8049.2.a.c | $119$ | $64.272$ | None | \(11\) | \(-119\) | \(17\) | \(10\) | $+$ | $-$ | |||
8049.2.a.d | $129$ | $64.272$ | None | \(8\) | \(129\) | \(11\) | \(40\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8049))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8049)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2683))\)\(^{\oplus 2}\)