Defining parameters
Level: | \( N \) | \(=\) | \( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7280.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 59 \) | ||
Sturm bound: | \(2688\) | ||
Trace bound: | \(23\) | ||
Distinguishing \(T_p\): | \(3\), \(11\), \(17\), \(19\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7280))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1368 | 144 | 1224 |
Cusp forms | 1321 | 144 | 1177 |
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.
\(2\) | \(5\) | \(7\) | \(13\) | Fricke | Dim. |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(10\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(8\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(10\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(8\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(8\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(10\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(8\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(10\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(11\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(8\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(5\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(12\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(8\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(11\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(12\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(5\) |
Plus space | \(+\) | \(62\) | |||
Minus space | \(-\) | \(82\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7280))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7280))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(7280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(910))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1040))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1820))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3640))\)\(^{\oplus 2}\)