Defining parameters
Level: | \( N \) | \(=\) | \( 5312 = 2^{6} \cdot 83 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5312.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 48 \) | ||
Sturm bound: | \(1344\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5312))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 684 | 164 | 520 |
Cusp forms | 661 | 164 | 497 |
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.
\(2\) | \(83\) | Fricke | Dim. |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(37\) |
\(+\) | \(-\) | \(-\) | \(46\) |
\(-\) | \(+\) | \(-\) | \(45\) |
\(-\) | \(-\) | \(+\) | \(36\) |
Plus space | \(+\) | \(73\) | |
Minus space | \(-\) | \(91\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5312))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5312))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5312)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(83))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(166))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(332))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(664))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1328))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2656))\)\(^{\oplus 2}\)