Defining parameters
Level: | \( N \) | \(=\) | \( 119 = 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 119.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(119))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 9 | 5 |
Cusp forms | 11 | 9 | 2 |
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.
\(7\) | \(17\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(-\) | $-$ | \(5\) |
\(-\) | \(+\) | $-$ | \(4\) |
Plus space | \(+\) | \(0\) | |
Minus space | \(-\) | \(9\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(119))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 7 | 17 | |||||||
119.2.a.a | $4$ | $0.950$ | 4.4.9301.1 | None | \(-1\) | \(2\) | \(2\) | \(4\) | $-$ | $+$ | \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\) | |
119.2.a.b | $5$ | $0.950$ | 5.5.453749.1 | None | \(2\) | \(-2\) | \(0\) | \(-5\) | $+$ | $-$ | \(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(119))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(119)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)