Defining parameters
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(1368\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8003))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 686 | 651 | 35 |
Cusp forms | 683 | 651 | 32 |
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.
\(53\) | \(151\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(153\) |
\(+\) | \(-\) | $-$ | \(172\) |
\(-\) | \(+\) | $-$ | \(179\) |
\(-\) | \(-\) | $+$ | \(147\) |
Plus space | \(+\) | \(300\) | |
Minus space | \(-\) | \(351\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8003))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 53 | 151 | |||||||
8003.2.a.a | $147$ | $63.904$ | None | \(-6\) | \(-23\) | \(-25\) | \(-33\) | $-$ | $-$ | |||
8003.2.a.b | $153$ | $63.904$ | None | \(-9\) | \(-17\) | \(-31\) | \(-17\) | $+$ | $+$ | |||
8003.2.a.c | $172$ | $63.904$ | None | \(8\) | \(25\) | \(27\) | \(31\) | $+$ | $-$ | |||
8003.2.a.d | $179$ | $63.904$ | None | \(8\) | \(15\) | \(27\) | \(23\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8003))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8003)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(151))\)\(^{\oplus 2}\)