Defining parameters
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(18\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(17))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 14 | 4 |
Cusp forms | 16 | 14 | 2 |
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 |
---|---|
\(+\) | \(8\) |
\(-\) | \(6\) |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(17))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 17 | |||||||
17.12.a.a | $6$ | $13.062$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(-9\) | \(-476\) | \(-12884\) | \(-23436\) | $-$ | \(q+(-2+\beta _{1})q^{2}+(-79+\beta _{2})q^{3}+(767+\cdots)q^{4}+\cdots\) | |
17.12.a.b | $8$ | $13.062$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(55\) | \(496\) | \(8592\) | \(95288\) | $+$ | \(q+(7-\beta _{1})q^{2}+(62-\beta _{1}+\beta _{3})q^{3}+(1344+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(17))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_0(17)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)