Defining parameters
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(15))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 16 | 4 | 12 |
Cusp forms | 12 | 4 | 8 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(3\) | |
Minus space | \(-\) | \(1\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(15))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 5 | |||||||
15.8.a.a | $1$ | $4.686$ | \(\Q\) | None | \(-22\) | \(27\) | \(-125\) | \(-420\) | $-$ | $+$ | \(q-22q^{2}+3^{3}q^{3}+356q^{4}-5^{3}q^{5}+\cdots\) | |
15.8.a.b | $1$ | $4.686$ | \(\Q\) | None | \(-13\) | \(-27\) | \(-125\) | \(1380\) | $+$ | $+$ | \(q-13q^{2}-3^{3}q^{3}+41q^{4}-5^{3}q^{5}+\cdots\) | |
15.8.a.c | $2$ | $4.686$ | \(\Q(\sqrt{601}) \) | None | \(7\) | \(54\) | \(250\) | \(1304\) | $-$ | $-$ | \(q+(4-\beta )q^{2}+3^{3}q^{3}+(38-7\beta )q^{4}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(15))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(15)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)