Defining parameters
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 73 \) | ||
Sturm bound: | \(2912\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7098))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1512 | 154 | 1358 |
Cusp forms | 1401 | 154 | 1247 |
Eisenstein series | 111 | 0 | 111 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(7\) | \(13\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(11\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(9\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(10\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(9\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(10\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(9\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(11\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(9\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(13\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(6\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(7\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(12\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(7\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(12\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(13\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(6\) |
Plus space | \(+\) | \(66\) | |||
Minus space | \(-\) | \(88\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7098))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7098))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(7098)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2366))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3549))\)\(^{\oplus 2}\)