Defining parameters
Level: | \( N \) | \(=\) | \( 6192 = 2^{4} \cdot 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6192.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 55 \) | ||
Sturm bound: | \(2112\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6192))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1080 | 105 | 975 |
Cusp forms | 1033 | 105 | 928 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(43\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(8\) |
\(+\) | \(+\) | \(-\) | $-$ | \(14\) |
\(+\) | \(-\) | \(+\) | $-$ | \(17\) |
\(+\) | \(-\) | \(-\) | $+$ | \(14\) |
\(-\) | \(+\) | \(+\) | $-$ | \(10\) |
\(-\) | \(+\) | \(-\) | $+$ | \(10\) |
\(-\) | \(-\) | \(+\) | $+$ | \(16\) |
\(-\) | \(-\) | \(-\) | $-$ | \(16\) |
Plus space | \(+\) | \(48\) | ||
Minus space | \(-\) | \(57\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6192))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6192))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6192)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(129))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(172))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(258))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(344))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(387))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(516))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(688))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(774))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1032))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1548))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2064))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3096))\)\(^{\oplus 2}\)