Defining parameters
Level: | \( N \) | \(=\) | \( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3762.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 38 \) | ||
Sturm bound: | \(1440\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(13\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3762))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 736 | 76 | 660 |
Cusp forms | 705 | 76 | 629 |
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.
\(2\) | \(3\) | \(11\) | \(19\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(5\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(5\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(3\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(4\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(7\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(5\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(5\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(5\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(7\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(8\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(3\) |
Plus space | \(+\) | \(32\) | |||
Minus space | \(-\) | \(44\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3762))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3762))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3762)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(418))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(627))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1254))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1881))\)\(^{\oplus 2}\)