Defining parameters
Level: | \( N \) | \(=\) | \( 9801 = 3^{4} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9801.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 70 \) | ||
Sturm bound: | \(2376\) | ||
Trace bound: | \(14\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(7\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9801))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1260 | 454 | 806 |
Cusp forms | 1117 | 418 | 699 |
Eisenstein series | 143 | 36 | 107 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(98\) |
\(+\) | \(-\) | $-$ | \(110\) |
\(-\) | \(+\) | $-$ | \(110\) |
\(-\) | \(-\) | $+$ | \(100\) |
Plus space | \(+\) | \(198\) | |
Minus space | \(-\) | \(220\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9801))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9801))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9801)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(297))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(891))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3267))\)\(^{\oplus 2}\)