Defining parameters
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 48 \) | ||
Sturm bound: | \(1920\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4560))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 984 | 72 | 912 |
Cusp forms | 937 | 72 | 865 |
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.
\(2\) | \(3\) | \(5\) | \(19\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(4\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(5\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(6\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(3\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(5\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(4\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(6\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(5\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(4\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(6\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(4\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(6\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(3\) |
Plus space | \(+\) | \(28\) | |||
Minus space | \(-\) | \(44\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4560))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4560))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4560)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(570))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(760))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1140))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2280))\)\(^{\oplus 2}\)