Defining parameters
Level: | \( N \) | \(=\) | \( 520 = 2^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 520.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(520))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 260 | 36 | 224 |
Cusp forms | 244 | 36 | 208 |
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.
\(2\) | \(5\) | \(13\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(5\) |
\(+\) | \(+\) | \(-\) | $-$ | \(4\) |
\(+\) | \(-\) | \(+\) | $-$ | \(4\) |
\(+\) | \(-\) | \(-\) | $+$ | \(6\) |
\(-\) | \(+\) | \(+\) | $-$ | \(4\) |
\(-\) | \(+\) | \(-\) | $+$ | \(4\) |
\(-\) | \(-\) | \(+\) | $+$ | \(4\) |
\(-\) | \(-\) | \(-\) | $-$ | \(5\) |
Plus space | \(+\) | \(19\) | ||
Minus space | \(-\) | \(17\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(520))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(520))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(520)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 2}\)