Defining parameters
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(117))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 5 | 13 |
Cusp forms | 11 | 5 | 6 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(13\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(-\) | \(-\) | \(2\) |
\(-\) | \(+\) | \(-\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(1\) |
Plus space | \(+\) | \(1\) | |
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(117))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 13 | |||||||
117.2.a.a | $1$ | $0.934$ | \(\Q\) | None | \(-1\) | \(0\) | \(-2\) | \(-4\) | $-$ | $-$ | \(q-q^{2}-q^{4}-2q^{5}-4q^{7}+3q^{8}+2q^{10}+\cdots\) | |
117.2.a.b | $2$ | $0.934$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(0\) | \(0\) | \(4\) | $+$ | $-$ | \(q+\beta q^{2}+q^{4}+2q^{7}-\beta q^{8}-2\beta q^{11}+\cdots\) | |
117.2.a.c | $2$ | $0.934$ | \(\Q(\sqrt{2}) \) | None | \(2\) | \(0\) | \(0\) | \(0\) | $-$ | $+$ | \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2\beta q^{5}-2\beta q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(117))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(117)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 2}\)