Defining parameters
Level: | \( N \) | \(=\) | \( 6035 = 5 \cdot 17 \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6035.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(1296\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6035))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 652 | 375 | 277 |
Cusp forms | 645 | 375 | 270 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | \(17\) | \(71\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(44\) |
\(+\) | \(+\) | \(-\) | $-$ | \(49\) |
\(+\) | \(-\) | \(+\) | $-$ | \(49\) |
\(+\) | \(-\) | \(-\) | $+$ | \(44\) |
\(-\) | \(+\) | \(+\) | $-$ | \(59\) |
\(-\) | \(+\) | \(-\) | $+$ | \(36\) |
\(-\) | \(-\) | \(+\) | $+$ | \(36\) |
\(-\) | \(-\) | \(-\) | $-$ | \(58\) |
Plus space | \(+\) | \(160\) | ||
Minus space | \(-\) | \(215\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6035))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | 17 | 71 | |||||||
6035.2.a.a | $36$ | $48.190$ | None | \(-3\) | \(-8\) | \(36\) | \(-7\) | $-$ | $-$ | $+$ | |||
6035.2.a.b | $36$ | $48.190$ | None | \(-1\) | \(-4\) | \(36\) | \(-7\) | $-$ | $+$ | $-$ | |||
6035.2.a.c | $44$ | $48.190$ | None | \(-4\) | \(-4\) | \(-44\) | \(-5\) | $+$ | $+$ | $+$ | |||
6035.2.a.d | $44$ | $48.190$ | None | \(-2\) | \(-8\) | \(-44\) | \(-13\) | $+$ | $-$ | $-$ | |||
6035.2.a.e | $49$ | $48.190$ | None | \(1\) | \(10\) | \(-49\) | \(15\) | $+$ | $-$ | $+$ | |||
6035.2.a.f | $49$ | $48.190$ | None | \(3\) | \(6\) | \(-49\) | \(11\) | $+$ | $+$ | $-$ | |||
6035.2.a.g | $58$ | $48.190$ | None | \(1\) | \(6\) | \(58\) | \(13\) | $-$ | $-$ | $-$ | |||
6035.2.a.h | $59$ | $48.190$ | None | \(2\) | \(6\) | \(59\) | \(9\) | $-$ | $+$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6035))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6035)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(71))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(355))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1207))\)\(^{\oplus 2}\)