Defining parameters
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(198\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(197))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 183 | 179 | 4 |
Cusp forms | 181 | 179 | 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.
\(197\) | Dim |
---|---|
\(+\) | \(92\) |
\(-\) | \(87\) |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(197))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 197 | |||||||
197.12.a.a | $87$ | $151.364$ | None | \(-96\) | \(-2926\) | \(-20896\) | \(-231933\) | $-$ | |||
197.12.a.b | $92$ | $151.364$ | None | \(64\) | \(2420\) | \(16604\) | \(305891\) | $+$ |
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(197))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_0(197)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)