Defining parameters
Level: | \( N \) | \(=\) | \( 3520 = 2^{6} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3520.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 52 \) | ||
Sturm bound: | \(1152\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(13\), \(17\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3520))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 600 | 80 | 520 |
Cusp forms | 553 | 80 | 473 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | \(11\) | Fricke | Dim. |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(10\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(12\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(10\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(8\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(10\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(8\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(10\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(12\) |
Plus space | \(+\) | \(36\) | ||
Minus space | \(-\) | \(44\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3520))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3520))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3520)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(880))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1760))\)\(^{\oplus 2}\)