Defining parameters
Level: | \( N \) | \(=\) | \( 2312 = 2^{3} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2312.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 19 \) | ||
Sturm bound: | \(1224\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2312))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 954 | 203 | 751 |
Cusp forms | 882 | 203 | 679 |
Eisenstein series | 72 | 0 | 72 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(17\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(53\) |
\(+\) | \(-\) | $-$ | \(48\) |
\(-\) | \(+\) | $-$ | \(50\) |
\(-\) | \(-\) | $+$ | \(52\) |
Plus space | \(+\) | \(105\) | |
Minus space | \(-\) | \(98\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2312))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2312))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(2312)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 2}\)