Defining parameters
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(18))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 25 | 2 | 23 |
Cusp forms | 17 | 2 | 15 |
Eisenstein series | 8 | 0 | 8 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(1\) | |
Minus space | \(-\) | \(1\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(18))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
18.8.a.a | $1$ | $5.623$ | \(\Q\) | None | \(-8\) | \(0\) | \(114\) | \(-1576\) | $+$ | $-$ | \(q-8q^{2}+2^{6}q^{4}+114q^{5}-1576q^{7}+\cdots\) | |
18.8.a.b | $1$ | $5.623$ | \(\Q\) | None | \(8\) | \(0\) | \(210\) | \(1016\) | $-$ | $-$ | \(q+8q^{2}+2^{6}q^{4}+210q^{5}+1016q^{7}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)