Defining parameters
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 18 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(930))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 584 | 60 | 524 |
Cusp forms | 568 | 60 | 508 |
Eisenstein series | 16 | 0 | 16 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | \(31\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(4\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(4\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(4\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(3\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(3\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(5\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(4\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(3\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(3\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(4\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(5\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(3\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(5\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(6\) |
Plus space | \(+\) | \(36\) | |||
Minus space | \(-\) | \(24\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(930))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(930))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(930)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 2}\)