Defining parameters
Level: | \( N \) | \(=\) | \( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1428.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1428))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 300 | 16 | 284 |
Cusp forms | 277 | 16 | 261 |
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.
\(2\) | \(3\) | \(7\) | \(17\) | Fricke | Dim |
---|---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(2\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(2\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(1\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(3\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(2\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(6\) | |||
Minus space | \(-\) | \(10\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1428))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1428))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1428)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(714))\)\(^{\oplus 2}\)