Defining parameters
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(115))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 7 | 7 |
Cusp forms | 11 | 7 | 4 |
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.
\(5\) | \(23\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(+\) | $-$ | \(4\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(5\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(115))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | 23 | |||||||
115.2.a.a | $1$ | $0.918$ | \(\Q\) | None | \(2\) | \(0\) | \(-1\) | \(1\) | $+$ | $-$ | \(q+2q^{2}+2q^{4}-q^{5}+q^{7}-3q^{9}-2q^{10}+\cdots\) | |
115.2.a.b | $2$ | $0.918$ | \(\Q(\sqrt{5}) \) | None | \(-3\) | \(-2\) | \(-2\) | \(-2\) | $+$ | $+$ | \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}-q^{5}+\cdots\) | |
115.2.a.c | $4$ | $0.918$ | 4.4.15317.1 | None | \(2\) | \(-2\) | \(4\) | \(-3\) | $-$ | $+$ | \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(115))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(115)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)