Defining parameters
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(2016\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6012))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1020 | 68 | 952 |
Cusp forms | 997 | 68 | 929 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(167\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | $-$ | \(13\) |
\(-\) | \(+\) | \(-\) | $+$ | \(13\) |
\(-\) | \(-\) | \(+\) | $+$ | \(21\) |
\(-\) | \(-\) | \(-\) | $-$ | \(21\) |
Plus space | \(+\) | \(34\) | ||
Minus space | \(-\) | \(34\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6012))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6012))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(501))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(668))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1002))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1503))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2004))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3006))\)\(^{\oplus 2}\)