Defining parameters
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(16))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 25 | 6 | 19 |
Cusp forms | 19 | 5 | 14 |
Eisenstein series | 6 | 1 | 5 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | Dim |
---|---|
\(+\) | \(3\) |
\(-\) | \(2\) |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
16.12.a.a | $1$ | $12.293$ | \(\Q\) | None | \(0\) | \(-252\) | \(4830\) | \(16744\) | $-$ | \(q-252q^{3}+4830q^{5}+16744q^{7}+\cdots\) | |
16.12.a.b | $1$ | $12.293$ | \(\Q\) | None | \(0\) | \(36\) | \(-3490\) | \(55464\) | $+$ | \(q+6^{2}q^{3}-3490q^{5}+55464q^{7}-175851q^{9}+\cdots\) | |
16.12.a.c | $1$ | $12.293$ | \(\Q\) | None | \(0\) | \(516\) | \(-10530\) | \(-49304\) | $-$ | \(q+516q^{3}-10530q^{5}-49304q^{7}+\cdots\) | |
16.12.a.d | $2$ | $12.293$ | \(\Q(\sqrt{109}) \) | None | \(0\) | \(-56\) | \(7868\) | \(-91056\) | $+$ | \(q+(-28-\beta )q^{3}+(3934-12\beta )q^{5}+\cdots\) |
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)