Defining parameters
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 30 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1232))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 588 | 90 | 498 |
Cusp forms | 564 | 90 | 474 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(11\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(12\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(9\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(14\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(10\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(12\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(12\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(10\) |
Plus space | \(+\) | \(49\) | ||
Minus space | \(-\) | \(41\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1232))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1232))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1232)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 2}\)