Defining parameters
Level: | \( N \) | \(=\) | \( 134 = 2 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 134.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(34\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(134))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 19 | 6 | 13 |
Cusp forms | 16 | 6 | 10 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(67\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(-\) | $-$ | \(3\) |
\(-\) | \(+\) | $-$ | \(3\) |
Plus space | \(+\) | \(0\) | |
Minus space | \(-\) | \(6\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(134))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 67 | |||||||
134.2.a.a | $3$ | $1.070$ | 3.3.473.1 | None | \(-3\) | \(1\) | \(3\) | \(0\) | $+$ | $-$ | \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(1+\beta _{1})q^{5}-\beta _{2}q^{6}+\cdots\) | |
134.2.a.b | $3$ | $1.070$ | \(\Q(\zeta_{18})^+\) | None | \(3\) | \(3\) | \(-3\) | \(0\) | $-$ | $+$ | \(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(134))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(134)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 2}\)