Defining parameters
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(1632\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4020))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 828 | 44 | 784 |
Cusp forms | 805 | 44 | 761 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | \(67\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(40\) | \(0\) | \(40\) | \(39\) | \(0\) | \(39\) | \(1\) | \(0\) | \(1\) | |||
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(63\) | \(0\) | \(63\) | \(61\) | \(0\) | \(61\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(61\) | \(0\) | \(61\) | \(59\) | \(0\) | \(59\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(44\) | \(0\) | \(44\) | \(42\) | \(0\) | \(42\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(45\) | \(0\) | \(45\) | \(43\) | \(0\) | \(43\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(58\) | \(0\) | \(58\) | \(56\) | \(0\) | \(56\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(62\) | \(0\) | \(62\) | \(60\) | \(0\) | \(60\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(43\) | \(0\) | \(43\) | \(41\) | \(0\) | \(41\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(50\) | \(7\) | \(43\) | \(49\) | \(7\) | \(42\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(54\) | \(4\) | \(50\) | \(53\) | \(4\) | \(49\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(56\) | \(5\) | \(51\) | \(55\) | \(5\) | \(50\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(46\) | \(6\) | \(40\) | \(45\) | \(6\) | \(39\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(45\) | \(5\) | \(40\) | \(44\) | \(5\) | \(39\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(59\) | \(6\) | \(53\) | \(58\) | \(6\) | \(52\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(55\) | \(7\) | \(48\) | \(54\) | \(7\) | \(47\) | \(1\) | \(0\) | \(1\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(47\) | \(4\) | \(43\) | \(46\) | \(4\) | \(42\) | \(1\) | \(0\) | \(1\) | |||
Plus space | \(+\) | \(406\) | \(18\) | \(388\) | \(395\) | \(18\) | \(377\) | \(11\) | \(0\) | \(11\) | ||||||
Minus space | \(-\) | \(422\) | \(26\) | \(396\) | \(410\) | \(26\) | \(384\) | \(12\) | \(0\) | \(12\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4020))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4020))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4020)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(201))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(268))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(335))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(402))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(670))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(804))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1005))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1340))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2010))\)\(^{\oplus 2}\)