Defining parameters
Level: | \( N \) | \(=\) | \( 9802 = 2 \cdot 13^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9802.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 46 \) | ||
Sturm bound: | \(2730\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9802))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1392 | 363 | 1029 |
Cusp forms | 1337 | 363 | 974 |
Eisenstein series | 55 | 0 | 55 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(13\) | \(29\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(49\) |
\(+\) | \(+\) | \(-\) | $-$ | \(45\) |
\(+\) | \(-\) | \(+\) | $-$ | \(41\) |
\(+\) | \(-\) | \(-\) | $+$ | \(47\) |
\(-\) | \(+\) | \(+\) | $-$ | \(49\) |
\(-\) | \(+\) | \(-\) | $+$ | \(38\) |
\(-\) | \(-\) | \(+\) | $+$ | \(41\) |
\(-\) | \(-\) | \(-\) | $-$ | \(53\) |
Plus space | \(+\) | \(175\) | ||
Minus space | \(-\) | \(188\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9802))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9802))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9802)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(377))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(754))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4901))\)\(^{\oplus 2}\)