Defining parameters
Level: | \( N \) | \(=\) | \( 93 = 3 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 93.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(42\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(93))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 34 | 16 | 18 |
Cusp forms | 30 | 16 | 14 |
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.
\(3\) | \(31\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(3\) |
\(+\) | \(-\) | $-$ | \(5\) |
\(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | $+$ | \(6\) |
Plus space | \(+\) | \(9\) | |
Minus space | \(-\) | \(7\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(93))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 31 | |||||||
93.4.a.a | $1$ | $5.487$ | \(\Q\) | None | \(3\) | \(-3\) | \(-9\) | \(-34\) | $+$ | $-$ | \(q+3q^{2}-3q^{3}+q^{4}-9q^{5}-9q^{6}+\cdots\) | |
93.4.a.b | $2$ | $5.487$ | \(\Q(\sqrt{29}) \) | None | \(-5\) | \(-6\) | \(8\) | \(-4\) | $+$ | $-$ | \(q+(-2-\beta )q^{2}-3q^{3}+(3+5\beta )q^{4}+\cdots\) | |
93.4.a.c | $2$ | $5.487$ | \(\Q(\sqrt{17}) \) | None | \(-3\) | \(6\) | \(-8\) | \(-37\) | $-$ | $+$ | \(q+(-1-\beta )q^{2}+3q^{3}+(-3+3\beta )q^{4}+\cdots\) | |
93.4.a.d | $2$ | $5.487$ | \(\Q(\sqrt{41}) \) | None | \(-1\) | \(-6\) | \(-11\) | \(29\) | $+$ | $-$ | \(q-\beta q^{2}-3q^{3}+(2+\beta )q^{4}+(-7+3\beta )q^{5}+\cdots\) | |
93.4.a.e | $3$ | $5.487$ | 3.3.2089.1 | None | \(3\) | \(-9\) | \(8\) | \(19\) | $+$ | $+$ | \(q+(1+\beta _{1})q^{2}-3q^{3}+(1+3\beta _{1}+2\beta _{2})q^{4}+\cdots\) | |
93.4.a.f | $6$ | $5.487$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(3\) | \(18\) | \(12\) | \(47\) | $-$ | $-$ | \(q+(1-\beta _{1})q^{2}+3q^{3}+(6+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(93))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(93)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)