Defining parameters
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(230))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 9 | 31 |
Cusp forms | 33 | 9 | 24 |
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.
\(2\) | \(5\) | \(23\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(-\) | \(-\) | \(2\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(2\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(3\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(2\) |
Plus space | \(+\) | \(0\) | ||
Minus space | \(-\) | \(9\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(230))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | 23 | |||||||
230.2.a.a | $2$ | $1.837$ | \(\Q(\sqrt{21}) \) | None | \(-2\) | \(-1\) | \(-2\) | \(1\) | $+$ | $+$ | $-$ | \(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\) | |
230.2.a.b | $2$ | $1.837$ | \(\Q(\sqrt{13}) \) | None | \(-2\) | \(3\) | \(2\) | \(3\) | $+$ | $-$ | $+$ | \(q-q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\) | |
230.2.a.c | $2$ | $1.837$ | \(\Q(\sqrt{5}) \) | None | \(2\) | \(1\) | \(2\) | \(1\) | $-$ | $-$ | $-$ | \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\) | |
230.2.a.d | $3$ | $1.837$ | 3.3.1101.1 | None | \(3\) | \(1\) | \(-3\) | \(3\) | $-$ | $+$ | $+$ | \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(230))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(230)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 2}\)