Defining parameters
Level: | \( N \) | \(=\) | \( 2002 = 2 \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2002.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 19 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2002))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 344 | 61 | 283 |
Cusp forms | 329 | 61 | 268 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | \(11\) | \(13\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(5\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(4\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(2\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(4\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(3\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(4\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(5\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(3\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(5\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(2\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(2\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(6\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(3\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(6\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(5\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(27\) | |||
Minus space | \(-\) | \(34\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2002))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2002))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1001))\)\(^{\oplus 2}\)