Defining parameters
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(1096\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6017))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 550 | 455 | 95 |
Cusp forms | 547 | 455 | 92 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(11\) | \(547\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(107\) |
\(+\) | \(-\) | $-$ | \(122\) |
\(-\) | \(+\) | $-$ | \(120\) |
\(-\) | \(-\) | $+$ | \(106\) |
Plus space | \(+\) | \(213\) | |
Minus space | \(-\) | \(242\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 11 | 547 | |||||||
6017.2.a.a | $1$ | $48.046$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(-2\) | $+$ | $-$ | \(q-2q^{4}-2q^{7}-3q^{9}-q^{11}-5q^{13}+\cdots\) | |
6017.2.a.b | $1$ | $48.046$ | \(\Q\) | None | \(0\) | \(2\) | \(4\) | \(2\) | $-$ | $+$ | \(q+2q^{3}-2q^{4}+4q^{5}+2q^{7}+q^{9}+\cdots\) | |
6017.2.a.c | $106$ | $48.046$ | None | \(-13\) | \(-15\) | \(-12\) | \(-66\) | $-$ | $-$ | |||
6017.2.a.d | $107$ | $48.046$ | None | \(-3\) | \(-18\) | \(-15\) | \(-54\) | $+$ | $+$ | |||
6017.2.a.e | $119$ | $48.046$ | None | \(15\) | \(15\) | \(6\) | \(72\) | $-$ | $+$ | |||
6017.2.a.f | $121$ | $48.046$ | None | \(2\) | \(18\) | \(13\) | \(56\) | $+$ | $-$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6017))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6017)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(547))\)\(^{\oplus 2}\)