Defining parameters
Level: | \( N \) | \(=\) | \( 9310 = 2 \cdot 5 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9310.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 69 \) | ||
Sturm bound: | \(3360\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(3\), \(11\), \(13\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9310))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1712 | 246 | 1466 |
Cusp forms | 1649 | 246 | 1403 |
Eisenstein series | 63 | 0 | 63 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | \(7\) | \(19\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(15\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(14\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(15\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(18\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(18\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(13\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(12\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(18\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(14\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(15\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(18\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(15\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(13\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(18\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(18\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(12\) |
Plus space | \(+\) | \(116\) | |||
Minus space | \(-\) | \(130\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9310))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9310))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9310)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(665))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1862))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4655))\)\(^{\oplus 2}\)