Defining parameters
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(16))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 41 | 10 | 31 |
Cusp forms | 35 | 9 | 26 |
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 |
---|---|
\(+\) | \(5\) |
\(-\) | \(4\) |
Trace form
Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
16.20.a.a | $1$ | $36.611$ | \(\Q\) | None | \(0\) | \(-50652\) | \(-2377410\) | \(16917544\) | $-$ | \(q-50652q^{3}-2377410q^{5}+16917544q^{7}+\cdots\) | |
16.20.a.b | $1$ | $36.611$ | \(\Q\) | None | \(0\) | \(36\) | \(-196290\) | \(35905576\) | $-$ | \(q+6^{2}q^{3}-196290q^{5}+35905576q^{7}+\cdots\) | |
16.20.a.c | $1$ | $36.611$ | \(\Q\) | None | \(0\) | \(13092\) | \(6546750\) | \(-96674264\) | $-$ | \(q+13092q^{3}+6546750q^{5}-96674264q^{7}+\cdots\) | |
16.20.a.d | $1$ | $36.611$ | \(\Q\) | None | \(0\) | \(53028\) | \(-5556930\) | \(44496424\) | $-$ | \(q+53028q^{3}-5556930q^{5}+44496424q^{7}+\cdots\) | |
16.20.a.e | $2$ | $36.611$ | \(\Q(\sqrt{1453}) \) | None | \(0\) | \(27912\) | \(1226620\) | \(-88510512\) | $+$ | \(q+(13956-\beta )q^{3}+(613310-44\beta )q^{5}+\cdots\) | |
16.20.a.f | $3$ | $36.611$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(0\) | \(-23732\) | \(2140218\) | \(-55851720\) | $+$ | \(q+(-7911+\beta _{1})q^{3}+(713429-70\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces
\( S_{20}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)