Defining parameters
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1038\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6031))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 520 | 487 | 33 |
Cusp forms | 517 | 487 | 30 |
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.
\(37\) | \(163\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(110\) |
\(+\) | \(-\) | $-$ | \(133\) |
\(-\) | \(+\) | $-$ | \(135\) |
\(-\) | \(-\) | $+$ | \(109\) |
Plus space | \(+\) | \(219\) | |
Minus space | \(-\) | \(268\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6031))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 37 | 163 | |||||||
6031.2.a.a | $1$ | $48.158$ | \(\Q\) | None | \(0\) | \(3\) | \(4\) | \(1\) | $-$ | $+$ | \(q+3q^{3}-2q^{4}+4q^{5}+q^{7}+6q^{9}+\cdots\) | |
6031.2.a.b | $109$ | $48.158$ | None | \(-11\) | \(-14\) | \(-28\) | \(-16\) | $-$ | $-$ | |||
6031.2.a.c | $110$ | $48.158$ | None | \(-9\) | \(0\) | \(-26\) | \(-4\) | $+$ | $+$ | |||
6031.2.a.d | $133$ | $48.158$ | None | \(14\) | \(8\) | \(34\) | \(8\) | $+$ | $-$ | |||
6031.2.a.e | $134$ | $48.158$ | None | \(9\) | \(7\) | \(22\) | \(11\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6031))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6031)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(163))\)\(^{\oplus 2}\)