Defining parameters
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1280))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 216 | 32 | 184 |
Cusp forms | 169 | 32 | 137 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(6\) |
\(+\) | \(-\) | \(-\) | \(10\) |
\(-\) | \(+\) | \(-\) | \(10\) |
\(-\) | \(-\) | \(+\) | \(6\) |
Plus space | \(+\) | \(12\) | |
Minus space | \(-\) | \(20\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1280))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1280))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1280)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(640))\)\(^{\oplus 2}\)