Defining parameters
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(30\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{30}(\Gamma_0(6))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 31 | 5 | 26 |
Cusp forms | 27 | 5 | 22 |
Eisenstein series | 4 | 0 | 4 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{30}^{\mathrm{new}}(\Gamma_0(6))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
6.30.a.a | $1$ | $31.967$ | \(\Q\) | None | \(-16384\) | \(-4782969\) | \(1951578750\) | \(-15\!\cdots\!92\) | $+$ | $+$ | \(q-2^{14}q^{2}-3^{14}q^{3}+2^{28}q^{4}+1951578750q^{5}+\cdots\) | |
6.30.a.b | $1$ | $31.967$ | \(\Q\) | None | \(-16384\) | \(4782969\) | \(-13482080250\) | \(-517740139336\) | $+$ | $-$ | \(q-2^{14}q^{2}+3^{14}q^{3}+2^{28}q^{4}-13482080250q^{5}+\cdots\) | |
6.30.a.c | $1$ | $31.967$ | \(\Q\) | None | \(16384\) | \(4782969\) | \(-21003872250\) | \(15\!\cdots\!32\) | $-$ | $-$ | \(q+2^{14}q^{2}+3^{14}q^{3}+2^{28}q^{4}-21003872250q^{5}+\cdots\) | |
6.30.a.d | $2$ | $31.967$ | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) | None | \(32768\) | \(-9565938\) | \(-6557946756\) | \(-11\!\cdots\!48\) | $-$ | $+$ | \(q+2^{14}q^{2}-3^{14}q^{3}+2^{28}q^{4}+(-3278973378+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{30}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces
\( S_{30}^{\mathrm{old}}(\Gamma_0(6)) \cong \) \(S_{30}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)