Defining parameters
Level: | \( N \) | \(=\) | \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6930.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 65 \) | ||
Sturm bound: | \(3456\) | ||
Trace bound: | \(23\) | ||
Distinguishing \(T_p\): | \(13\), \(17\), \(19\), \(23\), \(29\), \(31\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6930))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1760 | 100 | 1660 |
Cusp forms | 1697 | 100 | 1597 |
Eisenstein series | 63 | 0 | 63 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(3\) |
\(+\) | \(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(3\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(1\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(3\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(1\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(3\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(3\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(3\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(5\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(2\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(3\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(5\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(4\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(4\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(4\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(3\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(+\) | $-$ | \(3\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | $+$ | \(1\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | $+$ | \(3\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(-\) | $-$ | \(3\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | $+$ | \(3\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(-\) | $-$ | \(3\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | $+$ | \(1\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | $+$ | \(3\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(-\) | $-$ | \(5\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(+\) | $-$ | \(4\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | $+$ | \(3\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(+\) | $-$ | \(5\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | $+$ | \(2\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | $+$ | \(2\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(-\) | $-$ | \(6\) |
Plus space | \(+\) | \(42\) | ||||
Minus space | \(-\) | \(58\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6930))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6930))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6930)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(990))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1386))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3465))\)\(^{\oplus 2}\)