Defining parameters
Level: | \( N \) | \(=\) | \( 471 = 3 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 471.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(210\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(471))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 160 | 78 | 82 |
Cusp forms | 156 | 78 | 78 |
Eisenstein series | 4 | 0 | 4 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(157\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(22\) |
\(+\) | \(-\) | $-$ | \(17\) |
\(-\) | \(+\) | $-$ | \(14\) |
\(-\) | \(-\) | $+$ | \(25\) |
Plus space | \(+\) | \(47\) | |
Minus space | \(-\) | \(31\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(471))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 157 | |||||||
471.4.a.a | $14$ | $27.790$ | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) | None | \(-2\) | \(42\) | \(-32\) | \(-60\) | $-$ | $+$ | \(q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\) | |
471.4.a.b | $17$ | $27.790$ | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) | None | \(-2\) | \(-51\) | \(-28\) | \(10\) | $+$ | $-$ | \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\) | |
471.4.a.c | $22$ | $27.790$ | None | \(4\) | \(-66\) | \(32\) | \(-4\) | $+$ | $+$ | |||
471.4.a.d | $25$ | $27.790$ | None | \(4\) | \(75\) | \(28\) | \(94\) | $-$ | $-$ |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(471))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(471)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(157))\)\(^{\oplus 2}\)