Defining parameters
Level: | \( N \) | \(=\) | \( 5082 = 2 \cdot 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5082.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 59 \) | ||
Sturm bound: | \(2112\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\), \(13\), \(17\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5082))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1104 | 110 | 994 |
Cusp forms | 1009 | 110 | 899 |
Eisenstein series | 95 | 0 | 95 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(7\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(6\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(8\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(6\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(8\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(6\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(7\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(6\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(10\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(4\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(5\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(9\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(5\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(9\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(10\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(4\) |
Plus space | \(+\) | \(44\) | |||
Minus space | \(-\) | \(66\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5082))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5082))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5082)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(847))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1694))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\)\(^{\oplus 2}\)