Defining parameters
Level: | \( N \) | \(=\) | \( 3509 = 11^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3509.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 26 \) | ||
Sturm bound: | \(660\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(2\), \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3509))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 342 | 255 | 87 |
Cusp forms | 319 | 255 | 64 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(11\) | \(29\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(57\) |
\(+\) | \(-\) | $-$ | \(69\) |
\(-\) | \(+\) | $-$ | \(72\) |
\(-\) | \(-\) | $+$ | \(57\) |
Plus space | \(+\) | \(114\) | |
Minus space | \(-\) | \(141\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3509))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3509))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3509)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(319))\)\(^{\oplus 2}\)