Defining parameters
Level: | \( N \) | \(=\) | \( 51 = 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 51.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(51))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 8 | 12 |
Cusp forms | 16 | 8 | 8 |
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.
\(3\) | \(17\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(-\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(-\) | \(+\) | \(3\) |
Plus space | \(+\) | \(6\) | |
Minus space | \(-\) | \(2\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(51))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 17 | |||||||
51.4.a.a | $1$ | $3.009$ | \(\Q\) | None | \(-1\) | \(-3\) | \(16\) | \(34\) | $+$ | $+$ | \(q-q^{2}-3q^{3}-7q^{4}+2^{4}q^{5}+3q^{6}+\cdots\) | |
51.4.a.b | $1$ | $3.009$ | \(\Q\) | None | \(-1\) | \(3\) | \(-20\) | \(-2\) | $-$ | $+$ | \(q-q^{2}+3q^{3}-7q^{4}-20q^{5}-3q^{6}+\cdots\) | |
51.4.a.c | $1$ | $3.009$ | \(\Q\) | None | \(1\) | \(-3\) | \(-10\) | \(-8\) | $+$ | $-$ | \(q+q^{2}-3q^{3}-7q^{4}-10q^{5}-3q^{6}+\cdots\) | |
51.4.a.d | $2$ | $3.009$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-6\) | \(6\) | \(-8\) | $+$ | $+$ | \(q+\beta q^{2}-3q^{3}+10q^{4}+(3+4\beta )q^{5}+\cdots\) | |
51.4.a.e | $3$ | $3.009$ | 3.3.5912.1 | None | \(5\) | \(9\) | \(8\) | \(-8\) | $-$ | $-$ | \(q+(2-\beta _{1})q^{2}+3q^{3}+(5-2\beta _{1}+\beta _{2})q^{4}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(51))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(51)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)