Defining parameters
Level: | \( N \) | \(=\) | \( 3185 = 5 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3185.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 31 \) | ||
Sturm bound: | \(784\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(2\), \(3\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3185))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 408 | 164 | 244 |
Cusp forms | 377 | 164 | 213 |
Eisenstein series | 31 | 0 | 31 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | \(7\) | \(13\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(18\) |
\(+\) | \(+\) | \(-\) | $-$ | \(24\) |
\(+\) | \(-\) | \(+\) | $-$ | \(21\) |
\(+\) | \(-\) | \(-\) | $+$ | \(18\) |
\(-\) | \(+\) | \(+\) | $-$ | \(24\) |
\(-\) | \(+\) | \(-\) | $+$ | \(14\) |
\(-\) | \(-\) | \(+\) | $+$ | \(18\) |
\(-\) | \(-\) | \(-\) | $-$ | \(27\) |
Plus space | \(+\) | \(68\) | ||
Minus space | \(-\) | \(96\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3185))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3185))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3185)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 2}\)