Defining parameters
Level: | \( N \) | \(=\) | \( 3002 = 2 \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3002.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 14 \) | ||
Sturm bound: | \(800\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3002))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 404 | 117 | 287 |
Cusp forms | 397 | 117 | 280 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(19\) | \(79\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(14\) |
\(+\) | \(+\) | \(-\) | $-$ | \(16\) |
\(+\) | \(-\) | \(+\) | $-$ | \(17\) |
\(+\) | \(-\) | \(-\) | $+$ | \(11\) |
\(-\) | \(+\) | \(+\) | $-$ | \(18\) |
\(-\) | \(+\) | \(-\) | $+$ | \(10\) |
\(-\) | \(-\) | \(+\) | $+$ | \(10\) |
\(-\) | \(-\) | \(-\) | $-$ | \(21\) |
Plus space | \(+\) | \(45\) | ||
Minus space | \(-\) | \(72\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3002))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3002))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(79))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(158))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1501))\)\(^{\oplus 2}\)