Defining parameters
Level: | \( N \) | \(=\) | \( 4851 = 3^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4851.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 60 \) | ||
Sturm bound: | \(1344\) | ||
Trace bound: | \(23\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(13\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4851))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 704 | 172 | 532 |
Cusp forms | 641 | 172 | 469 |
Eisenstein series | 63 | 0 | 63 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(19\) |
\(+\) | \(+\) | \(-\) | $-$ | \(19\) |
\(+\) | \(-\) | \(+\) | $-$ | \(16\) |
\(+\) | \(-\) | \(-\) | $+$ | \(16\) |
\(-\) | \(+\) | \(+\) | $-$ | \(28\) |
\(-\) | \(+\) | \(-\) | $+$ | \(20\) |
\(-\) | \(-\) | \(+\) | $+$ | \(24\) |
\(-\) | \(-\) | \(-\) | $-$ | \(30\) |
Plus space | \(+\) | \(79\) | ||
Minus space | \(-\) | \(93\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4851))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4851))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4851)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1617))\)\(^{\oplus 2}\)