Defining parameters
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(378))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 84 | 8 | 76 |
Cusp forms | 61 | 8 | 53 |
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.
\(2\) | \(3\) | \(7\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(7\) | \(1\) | \(6\) | \(5\) | \(1\) | \(4\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(11\) | \(1\) | \(10\) | \(8\) | \(1\) | \(7\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(13\) | \(1\) | \(12\) | \(10\) | \(1\) | \(9\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(11\) | \(1\) | \(10\) | \(8\) | \(1\) | \(7\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(11\) | \(2\) | \(9\) | \(8\) | \(2\) | \(6\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(10\) | \(0\) | \(10\) | \(7\) | \(0\) | \(7\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(11\) | \(0\) | \(11\) | \(8\) | \(0\) | \(8\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(10\) | \(2\) | \(8\) | \(7\) | \(2\) | \(5\) | \(3\) | \(0\) | \(3\) | |||
Plus space | \(+\) | \(39\) | \(2\) | \(37\) | \(28\) | \(2\) | \(26\) | \(11\) | \(0\) | \(11\) | |||||
Minus space | \(-\) | \(45\) | \(6\) | \(39\) | \(33\) | \(6\) | \(27\) | \(12\) | \(0\) | \(12\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(378))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(378))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(378)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 2}\)