Defining parameters
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(196))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 4 | 36 |
Cusp forms | 17 | 4 | 13 |
Eisenstein series | 23 | 0 | 23 |
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 |
---|---|---|---|
\(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(1\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(196))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 7 | |||||||
196.2.a.a | $1$ | $1.565$ | \(\Q\) | None | \(0\) | \(-1\) | \(-3\) | \(0\) | $-$ | $-$ | \(q-q^{3}-3q^{5}-2q^{9}-3q^{11}-2q^{13}+\cdots\) | |
196.2.a.b | $1$ | $1.565$ | \(\Q\) | None | \(0\) | \(1\) | \(3\) | \(0\) | $-$ | $+$ | \(q+q^{3}+3q^{5}-2q^{9}-3q^{11}+2q^{13}+\cdots\) | |
196.2.a.c | $2$ | $1.565$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | $-$ | $+$ | \(q+2\beta q^{3}-\beta q^{5}+5q^{9}+4q^{11}-3\beta q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(196))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(196)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)