Defining parameters
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(105))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 52 | 12 | 40 |
Cusp forms | 44 | 12 | 32 |
Eisenstein series | 8 | 0 | 8 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(7\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(9\) | \(2\) | \(7\) | \(8\) | \(2\) | \(6\) | \(1\) | \(0\) | \(1\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(5\) | \(0\) | \(5\) | \(4\) | \(0\) | \(4\) | \(1\) | \(0\) | \(1\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(5\) | \(2\) | \(3\) | \(4\) | \(2\) | \(2\) | \(1\) | \(0\) | \(1\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(7\) | \(2\) | \(5\) | \(6\) | \(2\) | \(4\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(7\) | \(2\) | \(5\) | \(6\) | \(2\) | \(4\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(7\) | \(2\) | \(5\) | \(6\) | \(2\) | \(4\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(5\) | \(2\) | \(3\) | \(4\) | \(2\) | \(2\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(7\) | \(0\) | \(7\) | \(6\) | \(0\) | \(6\) | \(1\) | \(0\) | \(1\) | |||
Plus space | \(+\) | \(28\) | \(8\) | \(20\) | \(24\) | \(8\) | \(16\) | \(4\) | \(0\) | \(4\) | |||||
Minus space | \(-\) | \(24\) | \(4\) | \(20\) | \(20\) | \(4\) | \(16\) | \(4\) | \(0\) | \(4\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(105))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(105))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(105)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)