Defining parameters
Level: | \( N \) | \(=\) | \( 4592 = 2^{4} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4592.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 37 \) | ||
Sturm bound: | \(1344\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4592))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 684 | 120 | 564 |
Cusp forms | 661 | 120 | 541 |
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.
\(2\) | \(7\) | \(41\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(15\) |
\(+\) | \(+\) | \(-\) | $-$ | \(15\) |
\(+\) | \(-\) | \(+\) | $-$ | \(15\) |
\(+\) | \(-\) | \(-\) | $+$ | \(15\) |
\(-\) | \(+\) | \(+\) | $-$ | \(18\) |
\(-\) | \(+\) | \(-\) | $+$ | \(11\) |
\(-\) | \(-\) | \(+\) | $+$ | \(12\) |
\(-\) | \(-\) | \(-\) | $-$ | \(19\) |
Plus space | \(+\) | \(53\) | ||
Minus space | \(-\) | \(67\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4592))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4592))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4592)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(328))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(656))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1148))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2296))\)\(^{\oplus 2}\)