Defining parameters
Level: | \( N \) | \(=\) | \( 3971 = 11 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3971.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 24 \) | ||
Sturm bound: | \(760\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3971))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 400 | 284 | 116 |
Cusp forms | 361 | 284 | 77 |
Eisenstein series | 39 | 0 | 39 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(11\) | \(19\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(63\) |
\(+\) | \(-\) | \(-\) | \(78\) |
\(-\) | \(+\) | \(-\) | \(83\) |
\(-\) | \(-\) | \(+\) | \(60\) |
Plus space | \(+\) | \(123\) | |
Minus space | \(-\) | \(161\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3971))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3971))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3971)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 2}\)