Defining parameters
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 25 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(17\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1638))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 352 | 30 | 322 |
Cusp forms | 321 | 30 | 291 |
Eisenstein series | 31 | 0 | 31 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(7\) | \(13\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(1\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(1\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(2\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(3\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(2\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(3\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(2\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(1\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(1\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(2\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(1\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(3\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(12\) | |||
Minus space | \(-\) | \(18\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1638))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1638))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1638)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(819))\)\(^{\oplus 2}\)