Defining parameters
Level: | \( N \) | \(=\) | \( 1250 = 2 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1250.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 14 \) | ||
Sturm bound: | \(750\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1250))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 593 | 120 | 473 |
Cusp forms | 533 | 120 | 413 |
Eisenstein series | 60 | 0 | 60 |
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 |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(32\) |
\(+\) | \(-\) | \(-\) | \(28\) |
\(-\) | \(+\) | \(-\) | \(26\) |
\(-\) | \(-\) | \(+\) | \(34\) |
Plus space | \(+\) | \(66\) | |
Minus space | \(-\) | \(54\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1250))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1250))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1250)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(125))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(250))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(625))\)\(^{\oplus 2}\)