Defining parameters
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(6\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(17))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6 | 4 | 2 |
Cusp forms | 4 | 4 | 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.
\(17\) | Dim |
---|---|
\(+\) | \(3\) |
\(-\) | \(1\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(17))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 17 | |||||||
17.4.a.a | $1$ | $1.003$ | \(\Q\) | None | \(-3\) | \(-8\) | \(6\) | \(-28\) | $-$ | \(q-3q^{2}-8q^{3}+q^{4}+6q^{5}+24q^{6}+\cdots\) | |
17.4.a.b | $3$ | $1.003$ | 3.3.2636.1 | None | \(1\) | \(4\) | \(-8\) | \(22\) | $+$ | \(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\) |