Defining parameters
Level: | \( N \) | \(=\) | \( 8014 = 2 \cdot 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8014.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(2004\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8014))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1004 | 333 | 671 |
Cusp forms | 1001 | 333 | 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.
\(2\) | \(4007\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(76\) |
\(+\) | \(-\) | $-$ | \(91\) |
\(-\) | \(+\) | $-$ | \(90\) |
\(-\) | \(-\) | $+$ | \(76\) |
Plus space | \(+\) | \(152\) | |
Minus space | \(-\) | \(181\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8014))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 4007 | |||||||
8014.2.a.a | $2$ | $63.992$ | \(\Q(\sqrt{5}) \) | None | \(2\) | \(-2\) | \(1\) | \(-1\) | $-$ | $+$ | \(q+q^{2}-2\beta q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\) | |
8014.2.a.b | $76$ | $63.992$ | None | \(-76\) | \(2\) | \(-18\) | \(12\) | $+$ | $+$ | |||
8014.2.a.c | $76$ | $63.992$ | None | \(76\) | \(-20\) | \(-26\) | \(-34\) | $-$ | $-$ | |||
8014.2.a.d | $88$ | $63.992$ | None | \(88\) | \(22\) | \(25\) | \(33\) | $-$ | $+$ | |||
8014.2.a.e | $91$ | $63.992$ | None | \(-91\) | \(-2\) | \(22\) | \(-14\) | $+$ | $-$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8014))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4007))\)\(^{\oplus 2}\)