Defining parameters
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 28 \) | ||
Sturm bound: | \(1152\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1840))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 876 | 132 | 744 |
Cusp forms | 852 | 132 | 720 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | \(23\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(112\) | \(18\) | \(94\) | \(109\) | \(18\) | \(91\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(109\) | \(15\) | \(94\) | \(106\) | \(15\) | \(91\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(107\) | \(15\) | \(92\) | \(104\) | \(15\) | \(89\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(110\) | \(18\) | \(92\) | \(107\) | \(18\) | \(89\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(107\) | \(18\) | \(89\) | \(104\) | \(18\) | \(86\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(110\) | \(15\) | \(95\) | \(107\) | \(15\) | \(92\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(112\) | \(18\) | \(94\) | \(109\) | \(18\) | \(91\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(109\) | \(15\) | \(94\) | \(106\) | \(15\) | \(91\) | \(3\) | \(0\) | \(3\) | |||
Plus space | \(+\) | \(444\) | \(69\) | \(375\) | \(432\) | \(69\) | \(363\) | \(12\) | \(0\) | \(12\) | |||||
Minus space | \(-\) | \(432\) | \(63\) | \(369\) | \(420\) | \(63\) | \(357\) | \(12\) | \(0\) | \(12\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1840))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1840))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1840)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 2}\)