Defining parameters
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(160\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(608))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 18 | 70 |
Cusp forms | 73 | 18 | 55 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(19\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||
\(+\) | \(+\) | \(+\) | \(18\) | \(3\) | \(15\) | \(15\) | \(3\) | \(12\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(-\) | \(24\) | \(6\) | \(18\) | \(20\) | \(6\) | \(14\) | \(4\) | \(0\) | \(4\) | |||
\(-\) | \(+\) | \(-\) | \(26\) | \(6\) | \(20\) | \(22\) | \(6\) | \(16\) | \(4\) | \(0\) | \(4\) | |||
\(-\) | \(-\) | \(+\) | \(20\) | \(3\) | \(17\) | \(16\) | \(3\) | \(13\) | \(4\) | \(0\) | \(4\) | |||
Plus space | \(+\) | \(38\) | \(6\) | \(32\) | \(31\) | \(6\) | \(25\) | \(7\) | \(0\) | \(7\) | ||||
Minus space | \(-\) | \(50\) | \(12\) | \(38\) | \(42\) | \(12\) | \(30\) | \(8\) | \(0\) | \(8\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(608))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(608))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(608)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 2}\)