Defining parameters
Level: | \( N \) | \(=\) | \( 262 = 2 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 262.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(66\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(262))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 35 | 10 | 25 |
Cusp forms | 32 | 10 | 22 |
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.
\(2\) | \(131\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(3\) |
\(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(+\) | $-$ | \(4\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(4\) | |
Minus space | \(-\) | \(6\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(262))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 131 | |||||||
262.2.a.a | $1$ | $2.092$ | \(\Q\) | None | \(-1\) | \(0\) | \(0\) | \(-5\) | $+$ | $+$ | \(q-q^{2}+q^{4}-5q^{7}-q^{8}-3q^{9}+2q^{11}+\cdots\) | |
262.2.a.b | $1$ | $2.092$ | \(\Q\) | None | \(1\) | \(-2\) | \(-2\) | \(-3\) | $-$ | $-$ | \(q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}-3q^{7}+\cdots\) | |
262.2.a.c | $2$ | $2.092$ | \(\Q(\sqrt{13}) \) | None | \(-2\) | \(-1\) | \(-5\) | \(3\) | $+$ | $+$ | \(q-q^{2}-\beta q^{3}+q^{4}+(-3+\beta )q^{5}+\beta q^{6}+\cdots\) | |
262.2.a.d | $2$ | $2.092$ | \(\Q(\sqrt{2}) \) | None | \(-2\) | \(0\) | \(4\) | \(2\) | $+$ | $-$ | \(q-q^{2}+\beta q^{3}+q^{4}+(2-\beta )q^{5}-\beta q^{6}+\cdots\) | |
262.2.a.e | $2$ | $2.092$ | \(\Q(\sqrt{3}) \) | None | \(2\) | \(-2\) | \(2\) | \(4\) | $-$ | $+$ | \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots\) | |
262.2.a.f | $2$ | $2.092$ | \(\Q(\sqrt{5}) \) | None | \(2\) | \(3\) | \(-1\) | \(-1\) | $-$ | $+$ | \(q+q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\beta )q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(262))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(262)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(131))\)\(^{\oplus 2}\)