Defining parameters
Level: | \( N \) | \(=\) | \( 2106 = 2 \cdot 3^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2106.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 22 \) | ||
Sturm bound: | \(756\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2106))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 402 | 48 | 354 |
Cusp forms | 355 | 48 | 307 |
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.
\(2\) | \(3\) | \(13\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(6\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(7\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(6\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(5\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(8\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(3\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(4\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(9\) |
Plus space | \(+\) | \(18\) | ||
Minus space | \(-\) | \(30\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2106))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2106))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2106)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(351))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(702))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1053))\)\(^{\oplus 2}\)