Defining parameters
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 23 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(2\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1155))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 584 | 120 | 464 |
Cusp forms | 568 | 120 | 448 |
Eisenstein series | 16 | 0 | 16 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(8\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(8\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(7\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(9\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(7\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(7\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(8\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(6\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(6\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(8\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(9\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(5\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(9\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(7\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(6\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(10\) |
Plus space | \(+\) | \(68\) | |||
Minus space | \(-\) | \(52\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1155))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1155))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1155)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 2}\)