Defining parameters
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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 \(M_{16}(\Gamma_0(10))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 25 | 5 | 20 |
Cusp forms | 21 | 5 | 16 |
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.
\(2\) | \(5\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(1\) |
\(+\) | \(-\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(-\) | \(+\) | \(2\) |
Plus space | \(+\) | \(3\) | |
Minus space | \(-\) | \(2\) |
Trace form
Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(10))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | |||||||
10.16.a.a | $1$ | $14.269$ | \(\Q\) | None | \(-128\) | \(-5568\) | \(78125\) | \(2564996\) | $+$ | $-$ | \(q-2^{7}q^{2}-5568q^{3}+2^{14}q^{4}+5^{7}q^{5}+\cdots\) | |
10.16.a.b | $1$ | $14.269$ | \(\Q\) | None | \(-128\) | \(-918\) | \(-78125\) | \(-953554\) | $+$ | $+$ | \(q-2^{7}q^{2}-918q^{3}+2^{14}q^{4}-5^{7}q^{5}+\cdots\) | |
10.16.a.c | $1$ | $14.269$ | \(\Q\) | None | \(128\) | \(-1302\) | \(-78125\) | \(-90706\) | $-$ | $+$ | \(q+2^{7}q^{2}-1302q^{3}+2^{14}q^{4}-5^{7}q^{5}+\cdots\) | |
10.16.a.d | $2$ | $14.269$ | \(\Q(\sqrt{239569}) \) | None | \(256\) | \(-1844\) | \(156250\) | \(-984932\) | $-$ | $-$ | \(q+2^{7}q^{2}+(-922-\beta )q^{3}+2^{14}q^{4}+\cdots\) |
Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces
\( S_{16}^{\mathrm{old}}(\Gamma_0(10)) \simeq \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)