Defining parameters
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1504\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6008))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 756 | 188 | 568 |
Cusp forms | 749 | 188 | 561 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(751\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(44\) |
\(+\) | \(-\) | $-$ | \(50\) |
\(-\) | \(+\) | $-$ | \(50\) |
\(-\) | \(-\) | $+$ | \(44\) |
Plus space | \(+\) | \(88\) | |
Minus space | \(-\) | \(100\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6008))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 751 | |||||||
6008.2.a.a | $1$ | $47.974$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(-4\) | $+$ | $-$ | \(q-2q^{5}-4q^{7}-3q^{9}-q^{13}-6q^{17}+\cdots\) | |
6008.2.a.b | $44$ | $47.974$ | None | \(0\) | \(-14\) | \(7\) | \(-20\) | $+$ | $+$ | |||
6008.2.a.c | $44$ | $47.974$ | None | \(0\) | \(-4\) | \(-21\) | \(-10\) | $-$ | $-$ | |||
6008.2.a.d | $49$ | $47.974$ | None | \(0\) | \(14\) | \(-7\) | \(22\) | $+$ | $-$ | |||
6008.2.a.e | $50$ | $47.974$ | None | \(0\) | \(6\) | \(23\) | \(12\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6008))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(751))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1502))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3004))\)\(^{\oplus 2}\)