Defining parameters
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(231))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 11 | 25 |
Cusp forms | 29 | 11 | 18 |
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.
\(3\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(-\) | $-$ | \(3\) |
\(+\) | \(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(+\) | \(+\) | $-$ | \(3\) |
\(-\) | \(-\) | \(-\) | $-$ | \(2\) |
Plus space | \(+\) | \(0\) | ||
Minus space | \(-\) | \(11\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(231))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 7 | 11 | |||||||
231.2.a.a | $1$ | $1.845$ | \(\Q\) | None | \(-1\) | \(-1\) | \(-2\) | \(1\) | $+$ | $-$ | $+$ | \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\) | |
231.2.a.b | $2$ | $1.845$ | \(\Q(\sqrt{21}) \) | None | \(-1\) | \(-2\) | \(6\) | \(2\) | $+$ | $-$ | $+$ | \(q-\beta q^{2}-q^{3}+(3+\beta )q^{4}+3q^{5}+\beta q^{6}+\cdots\) | |
231.2.a.c | $2$ | $1.845$ | \(\Q(\sqrt{5}) \) | None | \(1\) | \(2\) | \(2\) | \(2\) | $-$ | $-$ | $-$ | \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\) | |
231.2.a.d | $3$ | $1.845$ | 3.3.837.1 | None | \(0\) | \(-3\) | \(0\) | \(-3\) | $+$ | $+$ | $-$ | \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\) | |
231.2.a.e | $3$ | $1.845$ | 3.3.229.1 | None | \(2\) | \(3\) | \(4\) | \(-3\) | $-$ | $+$ | $+$ | \(q+(1+\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+(1+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(231))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(231)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 2}\)