Defining parameters
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(16))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 29 | 7 | 22 |
Cusp forms | 23 | 6 | 17 |
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 |
---|---|
\(+\) | \(3\) |
\(-\) | \(3\) |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
16.14.a.a | $1$ | $17.157$ | \(\Q\) | None | \(0\) | \(-1236\) | \(-57450\) | \(-64232\) | $-$ | \(q-1236q^{3}-57450q^{5}-64232q^{7}+\cdots\) | |
16.14.a.b | $1$ | $17.157$ | \(\Q\) | None | \(0\) | \(-468\) | \(56214\) | \(-333032\) | $-$ | \(q-468q^{3}+56214q^{5}-333032q^{7}+\cdots\) | |
16.14.a.c | $1$ | $17.157$ | \(\Q\) | None | \(0\) | \(12\) | \(-4330\) | \(139992\) | $+$ | \(q+12q^{3}-4330q^{5}+139992q^{7}+\cdots\) | |
16.14.a.d | $1$ | $17.157$ | \(\Q\) | None | \(0\) | \(1836\) | \(3990\) | \(433432\) | $-$ | \(q+1836q^{3}+3990q^{5}+433432q^{7}+\cdots\) | |
16.14.a.e | $2$ | $17.157$ | \(\Q(\sqrt{781}) \) | None | \(0\) | \(-872\) | \(18476\) | \(-110928\) | $+$ | \(q+(-436-\beta )q^{3}+(9238+12\beta )q^{5}+\cdots\) |
Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces
\( S_{14}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)