Defining parameters
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(4\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(7))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 5 | 3 | 2 |
Cusp forms | 3 | 3 | 0 |
Eisenstein series | 2 | 0 | 2 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(7\) | Dim |
---|---|
\(+\) | \(1\) |
\(-\) | \(2\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(7))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 7 | |||||||
7.6.a.a | $1$ | $1.123$ | \(\Q\) | None | \(-10\) | \(-14\) | \(-56\) | \(-49\) | $+$ | \(q-10q^{2}-14q^{3}+68q^{4}-56q^{5}+\cdots\) | |
7.6.a.b | $2$ | $1.123$ | \(\Q(\sqrt{57}) \) | None | \(9\) | \(-6\) | \(-18\) | \(98\) | $-$ | \(q+(5-\beta )q^{2}+(-6+6\beta )q^{3}+(7-9\beta )q^{4}+\cdots\) |