Defining parameters
Level: | \( N \) | \(=\) | \( 2288 = 2^{4} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2288.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 27 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2288))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 348 | 60 | 288 |
Cusp forms | 325 | 60 | 265 |
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.
\(2\) | \(11\) | \(13\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(9\) |
\(+\) | \(+\) | \(-\) | $-$ | \(9\) |
\(+\) | \(-\) | \(+\) | $-$ | \(6\) |
\(+\) | \(-\) | \(-\) | $+$ | \(6\) |
\(-\) | \(+\) | \(+\) | $-$ | \(10\) |
\(-\) | \(+\) | \(-\) | $+$ | \(5\) |
\(-\) | \(-\) | \(+\) | $+$ | \(5\) |
\(-\) | \(-\) | \(-\) | $-$ | \(10\) |
Plus space | \(+\) | \(25\) | ||
Minus space | \(-\) | \(35\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2288))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2288))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2288)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1144))\)\(^{\oplus 2}\)