Defining parameters
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 30 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1078))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 520 | 103 | 417 |
Cusp forms | 488 | 103 | 385 |
Eisenstein series | 32 | 0 | 32 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(13\) |
\(+\) | \(+\) | \(-\) | $-$ | \(13\) |
\(+\) | \(-\) | \(+\) | $-$ | \(13\) |
\(+\) | \(-\) | \(-\) | $+$ | \(13\) |
\(-\) | \(+\) | \(+\) | $-$ | \(11\) |
\(-\) | \(+\) | \(-\) | $+$ | \(15\) |
\(-\) | \(-\) | \(+\) | $+$ | \(14\) |
\(-\) | \(-\) | \(-\) | $-$ | \(11\) |
Plus space | \(+\) | \(55\) | ||
Minus space | \(-\) | \(48\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1078))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1078))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1078)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 2}\)