Defining parameters
Level: | \( N \) | \(=\) | \( 7514 = 2 \cdot 13 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7514.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 53 \) | ||
Sturm bound: | \(2142\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7514))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1106 | 271 | 835 |
Cusp forms | 1035 | 271 | 764 |
Eisenstein series | 71 | 0 | 71 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(13\) | \(17\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(32\) |
\(+\) | \(+\) | \(-\) | $-$ | \(36\) |
\(+\) | \(-\) | \(+\) | $-$ | \(39\) |
\(+\) | \(-\) | \(-\) | $+$ | \(28\) |
\(-\) | \(+\) | \(+\) | $-$ | \(39\) |
\(-\) | \(+\) | \(-\) | $+$ | \(28\) |
\(-\) | \(-\) | \(+\) | $+$ | \(25\) |
\(-\) | \(-\) | \(-\) | $-$ | \(44\) |
Plus space | \(+\) | \(113\) | ||
Minus space | \(-\) | \(158\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7514))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7514))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(7514)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(221))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(442))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3757))\)\(^{\oplus 2}\)