Defining parameters
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(98))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 3 | 19 |
Cusp forms | 7 | 3 | 4 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(-\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(2\) |
Plus space | \(+\) | \(0\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(98))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 7 | |||||||
98.2.a.a | $1$ | $0.783$ | \(\Q\) | None | \(-1\) | \(2\) | \(0\) | \(0\) | $+$ | $-$ | \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\) | |
98.2.a.b | $2$ | $0.783$ | \(\Q(\sqrt{2}) \) | None | \(2\) | \(0\) | \(0\) | \(0\) | $-$ | $+$ | \(q+q^{2}+\beta q^{3}+q^{4}-2\beta q^{5}+\beta q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(98))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(98)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)