Defining parameters
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(30\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(10))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 31 | 5 | 26 |
Cusp forms | 27 | 5 | 22 |
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 \(S_{20}^{\mathrm{new}}(\Gamma_0(10))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | |||||||
10.20.a.a | $1$ | $22.882$ | \(\Q\) | None | \(-512\) | \(-26622\) | \(-1953125\) | \(-39884026\) | $+$ | $+$ | \(q-2^{9}q^{2}-26622q^{3}+2^{18}q^{4}-5^{9}q^{5}+\cdots\) | |
10.20.a.b | $1$ | $22.882$ | \(\Q\) | None | \(-512\) | \(38628\) | \(1953125\) | \(-144185776\) | $+$ | $-$ | \(q-2^{9}q^{2}+38628q^{3}+2^{18}q^{4}+5^{9}q^{5}+\cdots\) | |
10.20.a.c | $1$ | $22.882$ | \(\Q\) | None | \(512\) | \(24642\) | \(-1953125\) | \(-171901114\) | $-$ | $+$ | \(q+2^{9}q^{2}+24642q^{3}+2^{18}q^{4}-5^{9}q^{5}+\cdots\) | |
10.20.a.d | $2$ | $22.882$ | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) | None | \(1024\) | \(33724\) | \(3906250\) | \(83061292\) | $-$ | $-$ | \(q+2^{9}q^{2}+(16862-\beta )q^{3}+2^{18}q^{4}+\cdots\) |
Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces
\( S_{20}^{\mathrm{old}}(\Gamma_0(10)) \simeq \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)