Defining parameters
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(1062\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6001))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 532 | 469 | 63 |
Cusp forms | 529 | 469 | 60 |
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.
\(17\) | \(353\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(113\) |
\(+\) | \(-\) | $-$ | \(121\) |
\(-\) | \(+\) | $-$ | \(121\) |
\(-\) | \(-\) | $+$ | \(114\) |
Plus space | \(+\) | \(227\) | |
Minus space | \(-\) | \(242\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6001))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 17 | 353 | |||||||
6001.2.a.a | $113$ | $47.918$ | None | \(-11\) | \(-11\) | \(-19\) | \(11\) | $+$ | $+$ | |||
6001.2.a.b | $114$ | $47.918$ | None | \(-8\) | \(-23\) | \(-27\) | \(-53\) | $-$ | $-$ | |||
6001.2.a.c | $121$ | $47.918$ | None | \(9\) | \(13\) | \(21\) | \(-13\) | $+$ | $-$ | |||
6001.2.a.d | $121$ | $47.918$ | None | \(9\) | \(21\) | \(27\) | \(39\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6001))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6001)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(353))\)\(^{\oplus 2}\)