Defining parameters
Level: | \( N \) | \(=\) | \( 55 = 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 55.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(55))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 10 | 10 |
Cusp forms | 16 | 10 | 6 |
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.
\(5\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(-\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(4\) |
Plus space | \(+\) | \(7\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(55))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | 11 | |||||||
55.4.a.a | $1$ | $3.245$ | \(\Q\) | None | \(1\) | \(-3\) | \(-5\) | \(-9\) | $+$ | $-$ | \(q+q^{2}-3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots\) | |
55.4.a.b | $2$ | $3.245$ | \(\Q(\sqrt{17}) \) | None | \(-7\) | \(-3\) | \(10\) | \(-25\) | $-$ | $+$ | \(q+(-3-\beta )q^{2}+(-1-\beta )q^{3}+(5+7\beta )q^{4}+\cdots\) | |
55.4.a.c | $3$ | $3.245$ | 3.3.568.1 | None | \(5\) | \(-3\) | \(-15\) | \(-15\) | $+$ | $+$ | \(q+(1+\beta _{1}-\beta _{2})q^{2}+(-2-3\beta _{2})q^{3}+\cdots\) | |
55.4.a.d | $4$ | $3.245$ | 4.4.1539480.1 | None | \(1\) | \(9\) | \(20\) | \(9\) | $-$ | $-$ | \(q+\beta _{1}q^{2}+(2-\beta _{2})q^{3}+(5+\beta _{1}+\beta _{3})q^{4}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(55))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(55)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)