Defining parameters
Level: | \( N \) | \(=\) | \( 232 = 2^{3} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 232.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(232))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 34 | 7 | 27 |
Cusp forms | 27 | 7 | 20 |
Eisenstein series | 7 | 0 | 7 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(3\) |
\(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(3\) | |
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(232))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 29 | |||||||
232.2.a.a | $1$ | $1.853$ | \(\Q\) | None | \(0\) | \(-1\) | \(-3\) | \(2\) | $+$ | $+$ | \(q-q^{3}-3q^{5}+2q^{7}-2q^{9}-3q^{11}+\cdots\) | |
232.2.a.b | $1$ | $1.853$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(2\) | $-$ | $+$ | \(q+q^{3}+q^{5}+2q^{7}-2q^{9}+3q^{11}+\cdots\) | |
232.2.a.c | $2$ | $1.853$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(-8\) | $-$ | $-$ | \(q+(-1+\beta )q^{3}+(-1-2\beta )q^{5}-4q^{7}+\cdots\) | |
232.2.a.d | $3$ | $1.853$ | 3.3.568.1 | None | \(0\) | \(2\) | \(4\) | \(0\) | $+$ | $-$ | \(q+(1-\beta _{1})q^{3}+(1-\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(232))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(232)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 2}\)