Defining parameters
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(15))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 12 | 4 | 8 |
Cusp forms | 8 | 4 | 4 |
Eisenstein series | 4 | 0 | 4 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(+\) | $-$ | \(1\) |
Plus space | \(+\) | \(1\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(15))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 5 | |||||||
15.6.a.a | $1$ | $2.406$ | \(\Q\) | None | \(-2\) | \(-9\) | \(-25\) | \(-132\) | $+$ | $+$ | \(q-2q^{2}-9q^{3}-28q^{4}-5^{2}q^{5}+18q^{6}+\cdots\) | |
15.6.a.b | $1$ | $2.406$ | \(\Q\) | None | \(7\) | \(9\) | \(-25\) | \(12\) | $-$ | $+$ | \(q+7q^{2}+9q^{3}+17q^{4}-5^{2}q^{5}+63q^{6}+\cdots\) | |
15.6.a.c | $2$ | $2.406$ | \(\Q(\sqrt{409}) \) | None | \(-1\) | \(-18\) | \(50\) | \(-112\) | $+$ | $-$ | \(q-\beta q^{2}-9q^{3}+(70+\beta )q^{4}+5^{2}q^{5}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(15))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(15)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)