Defining parameters
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 34 \) | ||
Sturm bound: | \(970\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3549))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 512 | 156 | 356 |
Cusp forms | 457 | 156 | 301 |
Eisenstein series | 55 | 0 | 55 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(7\) | \(13\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(18\) |
\(+\) | \(+\) | \(-\) | $-$ | \(21\) |
\(+\) | \(-\) | \(+\) | $-$ | \(18\) |
\(+\) | \(-\) | \(-\) | $+$ | \(21\) |
\(-\) | \(+\) | \(+\) | $-$ | \(25\) |
\(-\) | \(+\) | \(-\) | $+$ | \(15\) |
\(-\) | \(-\) | \(+\) | $+$ | \(11\) |
\(-\) | \(-\) | \(-\) | $-$ | \(27\) |
Plus space | \(+\) | \(65\) | ||
Minus space | \(-\) | \(91\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3549))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3549))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3549)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 2}\)