Defining parameters
Level: | \( N \) | \(=\) | \( 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4368.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 45 \) | ||
Sturm bound: | \(1792\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4368))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 920 | 72 | 848 |
Cusp forms | 873 | 72 | 801 |
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.
\(2\) | \(3\) | \(7\) | \(13\) | Fricke | Dim. |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(6\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(4\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(3\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(5\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(6\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(2\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(7\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(4\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(5\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(6\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(6\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(5\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(2\) |
Plus space | \(+\) | \(32\) | |||
Minus space | \(-\) | \(40\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4368))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4368))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4368)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1092))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2184))\)\(^{\oplus 2}\)