Defining parameters
Level: | \( N \) | \(=\) | \( 116 = 2^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 116.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(30\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(116))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 3 | 15 |
Cusp forms | 13 | 3 | 10 |
Eisenstein series | 5 | 0 | 5 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(29\) | Fricke | Dim |
---|---|---|---|
\(-\) | \(+\) | $-$ | \(3\) |
Plus space | \(+\) | \(0\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(116))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 29 | |||||||
116.2.a.a | $1$ | $0.926$ | \(\Q\) | None | \(0\) | \(-3\) | \(3\) | \(4\) | $-$ | $+$ | \(q-3q^{3}+3q^{5}+4q^{7}+6q^{9}-q^{11}+\cdots\) | |
116.2.a.b | $1$ | $0.926$ | \(\Q\) | None | \(0\) | \(1\) | \(3\) | \(-4\) | $-$ | $+$ | \(q+q^{3}+3q^{5}-4q^{7}-2q^{9}+3q^{11}+\cdots\) | |
116.2.a.c | $1$ | $0.926$ | \(\Q\) | None | \(0\) | \(2\) | \(-2\) | \(4\) | $-$ | $+$ | \(q+2q^{3}-2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(116))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(116)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 2}\)