Defining parameters
| Level: | \( N \) | = | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Character orbit: | \([\chi]\) | = | 126.a (trivial) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(48\) | ||
| Trace bound: | \(2\) | ||
| Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(126))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 32 | 2 | 30 |
| Cusp forms | 17 | 2 | 15 |
| Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
| \(2\) | \(3\) | \(7\) | Fricke | Dim. |
|---|---|---|---|---|
| \(+\) | \(-\) | \(+\) | \(-\) | \(1\) |
| \(-\) | \(-\) | \(-\) | \(-\) | \(1\) |
| Plus space | \(+\) | \(0\) | ||
| Minus space | \(-\) | \(2\) | ||
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(126))\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 3 | 7 | |||||||
| 126.2.a.a | \(1\) | \(1.006\) | \(\Q\) | None | \(-1\) | \(0\) | \(2\) | \(-1\) | \(+\) | \(-\) | \(+\) | \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\) | |
| 126.2.a.b | \(1\) | \(1.006\) | \(\Q\) | None | \(1\) | \(0\) | \(0\) | \(1\) | \(-\) | \(-\) | \(-\) | \(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{13}+q^{14}+\cdots\) | |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(126))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(126)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 2}\)