Defining parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(5\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(3))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6 | 2 | 4 |
Cusp forms | 4 | 2 | 2 |
Eisenstein series | 2 | 0 | 2 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | Dim |
---|---|
\(+\) | \(1\) |
\(-\) | \(1\) |
Trace form
Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
3.16.a.a | $1$ | $4.281$ | \(\Q\) | None | \(-234\) | \(-2187\) | \(280710\) | \(-1373344\) | $+$ | \(q-234q^{2}-3^{7}q^{3}+21988q^{4}+280710q^{5}+\cdots\) | |
3.16.a.b | $1$ | $4.281$ | \(\Q\) | None | \(-72\) | \(2187\) | \(-221490\) | \(-2149000\) | $-$ | \(q-72q^{2}+3^{7}q^{3}-27584q^{4}-221490q^{5}+\cdots\) |
Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces
\( S_{16}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)