Defining parameters
Level: | \( N \) | \(=\) | \( 494 = 2 \cdot 13 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 494.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(140\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(494))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 74 | 17 | 57 |
Cusp forms | 67 | 17 | 50 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(13\) | \(19\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(+\) | \(-\) | $-$ | \(5\) |
\(+\) | \(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(+\) | \(+\) | $-$ | \(3\) |
\(-\) | \(-\) | \(+\) | $+$ | \(1\) |
\(-\) | \(-\) | \(-\) | $-$ | \(4\) |
Plus space | \(+\) | \(2\) | ||
Minus space | \(-\) | \(15\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(494))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(494))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(494)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(247))\)\(^{\oplus 2}\)