Defining parameters
Level: | \( N \) | \(=\) | \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7440.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 58 \) | ||
Sturm bound: | \(3072\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(17\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7440))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1560 | 120 | 1440 |
Cusp forms | 1513 | 120 | 1393 |
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.
\(2\) | \(3\) | \(5\) | \(31\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(7\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(8\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(9\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(6\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(8\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(7\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(6\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(9\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(8\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(7\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(6\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(9\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(7\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(8\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(9\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(6\) |
Plus space | \(+\) | \(52\) | |||
Minus space | \(-\) | \(68\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7440))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7440))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(7440)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(124))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(248))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(372))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(496))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(620))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(744))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(930))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1488))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1860))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3720))\)\(^{\oplus 2}\)