Defining parameters
Level: | \( N \) | \(=\) | \( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1716.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1716))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 348 | 20 | 328 |
Cusp forms | 325 | 20 | 305 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(11\) | \(13\) | Fricke | Dim. |
---|---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(3\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(2\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(4\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(4\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(3\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(1\) |
Plus space | \(+\) | \(6\) | |||
Minus space | \(-\) | \(14\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1716))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1716))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1716)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(858))\)\(^{\oplus 2}\)