Defining parameters
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 53 \) | ||
Sturm bound: | \(1440\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(3\), \(13\), \(17\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3850))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 744 | 94 | 650 |
Cusp forms | 697 | 94 | 603 |
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.
\(2\) | \(5\) | \(7\) | \(11\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(42\) | \(8\) | \(34\) | \(40\) | \(8\) | \(32\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(48\) | \(5\) | \(43\) | \(45\) | \(5\) | \(40\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(51\) | \(5\) | \(46\) | \(48\) | \(5\) | \(43\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(45\) | \(6\) | \(39\) | \(42\) | \(6\) | \(36\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(50\) | \(5\) | \(45\) | \(47\) | \(5\) | \(42\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(46\) | \(5\) | \(41\) | \(43\) | \(5\) | \(38\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(43\) | \(7\) | \(36\) | \(40\) | \(7\) | \(33\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(47\) | \(7\) | \(40\) | \(44\) | \(7\) | \(37\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(45\) | \(6\) | \(39\) | \(42\) | \(6\) | \(36\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(45\) | \(4\) | \(41\) | \(42\) | \(4\) | \(38\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(48\) | \(3\) | \(45\) | \(45\) | \(3\) | \(42\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(48\) | \(9\) | \(39\) | \(45\) | \(9\) | \(36\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(49\) | \(6\) | \(43\) | \(46\) | \(6\) | \(40\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(47\) | \(8\) | \(39\) | \(44\) | \(8\) | \(36\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(44\) | \(8\) | \(36\) | \(41\) | \(8\) | \(33\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(46\) | \(2\) | \(44\) | \(43\) | \(2\) | \(41\) | \(3\) | \(0\) | \(3\) | |||
Plus space | \(+\) | \(364\) | \(41\) | \(323\) | \(341\) | \(41\) | \(300\) | \(23\) | \(0\) | \(23\) | ||||||
Minus space | \(-\) | \(380\) | \(53\) | \(327\) | \(356\) | \(53\) | \(303\) | \(24\) | \(0\) | \(24\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3850))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3850))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3850)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1925))\)\(^{\oplus 2}\)