Defining parameters
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1082\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6019))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 542 | 463 | 79 |
Cusp forms | 539 | 463 | 76 |
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.
\(13\) | \(463\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(108\) |
\(+\) | \(-\) | $-$ | \(123\) |
\(-\) | \(+\) | $-$ | \(130\) |
\(-\) | \(-\) | $+$ | \(102\) |
Plus space | \(+\) | \(210\) | |
Minus space | \(-\) | \(253\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6019))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 13 | 463 | |||||||
6019.2.a.a | $1$ | $48.062$ | \(\Q\) | None | \(0\) | \(0\) | \(3\) | \(-3\) | $-$ | $-$ | \(q-2q^{4}+3q^{5}-3q^{7}-3q^{9}-q^{11}+\cdots\) | |
6019.2.a.b | $101$ | $48.062$ | None | \(-8\) | \(-13\) | \(-43\) | \(-1\) | $-$ | $-$ | |||
6019.2.a.c | $108$ | $48.062$ | None | \(-11\) | \(1\) | \(-40\) | \(-8\) | $+$ | $+$ | |||
6019.2.a.d | $123$ | $48.062$ | None | \(10\) | \(1\) | \(46\) | \(12\) | $+$ | $-$ | |||
6019.2.a.e | $130$ | $48.062$ | None | \(10\) | \(11\) | \(40\) | \(8\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6019))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6019)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(463))\)\(^{\oplus 2}\)