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
\( S_{2}^{\mathrm{old}}(\Gamma_0(126)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 2}\)