Defining parameters
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(200))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 42 | 5 | 37 |
Cusp forms | 19 | 5 | 14 |
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.
\(2\) | \(5\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(1\) | |
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(200))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | |||||||
200.2.a.a | $1$ | $1.597$ | \(\Q\) | None | \(0\) | \(-3\) | \(0\) | \(2\) | $+$ | $-$ | \(q-3q^{3}+2q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots\) | |
200.2.a.b | $1$ | $1.597$ | \(\Q\) | None | \(0\) | \(-2\) | \(0\) | \(-2\) | $-$ | $-$ | \(q-2q^{3}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots\) | |
200.2.a.c | $1$ | $1.597$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(4\) | $-$ | $+$ | \(q+4q^{7}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\) | |
200.2.a.d | $1$ | $1.597$ | \(\Q\) | None | \(0\) | \(2\) | \(0\) | \(2\) | $+$ | $-$ | \(q+2q^{3}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\) | |
200.2.a.e | $1$ | $1.597$ | \(\Q\) | None | \(0\) | \(3\) | \(0\) | \(-2\) | $-$ | $+$ | \(q+3q^{3}-2q^{7}+6q^{9}+q^{11}-4q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(200))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)