Defining parameters
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(30\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(18))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 31 | 4 | 27 |
Cusp forms | 23 | 4 | 19 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(2\) |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(18))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
18.10.a.a | $1$ | $9.271$ | \(\Q\) | None | \(-16\) | \(0\) | \(-870\) | \(-952\) | $+$ | $-$ | \(q-2^{4}q^{2}+2^{8}q^{4}-870q^{5}-952q^{7}+\cdots\) | |
18.10.a.b | $1$ | $9.271$ | \(\Q\) | None | \(-16\) | \(0\) | \(-384\) | \(5852\) | $+$ | $+$ | \(q-2^{4}q^{2}+2^{8}q^{4}-384q^{5}+5852q^{7}+\cdots\) | |
18.10.a.c | $1$ | $9.271$ | \(\Q\) | None | \(16\) | \(0\) | \(-2694\) | \(-3544\) | $-$ | $-$ | \(q+2^{4}q^{2}+2^{8}q^{4}-2694q^{5}-3544q^{7}+\cdots\) | |
18.10.a.d | $1$ | $9.271$ | \(\Q\) | None | \(16\) | \(0\) | \(384\) | \(5852\) | $-$ | $+$ | \(q+2^{4}q^{2}+2^{8}q^{4}+384q^{5}+5852q^{7}+\cdots\) |
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)