Defining parameters
Level: | \( N \) | \(=\) | \( 480 = 2^{5} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 480.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 18 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(480))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 304 | 24 | 280 |
Cusp forms | 272 | 24 | 248 |
Eisenstein series | 32 | 0 | 32 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(3\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(2\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(4\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(3\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(4\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(2\) |
Plus space | \(+\) | \(14\) | ||
Minus space | \(-\) | \(10\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(480))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(480))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(480)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)