Defining parameters
Level: | \( N \) | \(=\) | \( 2805 = 3 \cdot 5 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2805.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 22 \) | ||
Sturm bound: | \(864\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(7\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2805))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 440 | 105 | 335 |
Cusp forms | 425 | 105 | 320 |
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.
\(3\) | \(5\) | \(11\) | \(17\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(5\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(10\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(9\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(4\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(7\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(6\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(7\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(8\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(6\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(5\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(6\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(7\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(4\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(9\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(8\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(4\) |
Plus space | \(+\) | \(41\) | |||
Minus space | \(-\) | \(64\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2805))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2805))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2805)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(561))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(935))\)\(^{\oplus 2}\)