Defining parameters
Level: | \( N \) | \(=\) | \( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8022.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 27 \) | ||
Sturm bound: | \(3072\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8022))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1544 | 189 | 1355 |
Cusp forms | 1529 | 189 | 1340 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(7\) | \(191\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(13\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(11\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(9\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(15\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(13\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(11\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(9\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(15\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(13\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(10\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(12\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(11\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(8\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(15\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(17\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(7\) |
Plus space | \(+\) | \(85\) | |||
Minus space | \(-\) | \(104\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8022))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8022))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(573))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(191))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(382))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1146))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1337))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2674))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\)\(^{\oplus 2}\)