Defining parameters
Level: | \( N \) | \(=\) | \( 7872 = 2^{6} \cdot 3 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7872.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 70 \) | ||
Sturm bound: | \(2688\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7872))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1368 | 160 | 1208 |
Cusp forms | 1321 | 160 | 1161 |
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.
\(2\) | \(3\) | \(41\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(19\) |
\(+\) | \(+\) | \(-\) | $-$ | \(22\) |
\(+\) | \(-\) | \(+\) | $-$ | \(21\) |
\(+\) | \(-\) | \(-\) | $+$ | \(18\) |
\(-\) | \(+\) | \(+\) | $-$ | \(21\) |
\(-\) | \(+\) | \(-\) | $+$ | \(18\) |
\(-\) | \(-\) | \(+\) | $+$ | \(19\) |
\(-\) | \(-\) | \(-\) | $-$ | \(22\) |
Plus space | \(+\) | \(74\) | ||
Minus space | \(-\) | \(86\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7872))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7872))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(7872)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(123))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(246))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(328))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(492))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(656))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(984))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1968))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3936))\)\(^{\oplus 2}\)