Defining parameters
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(288))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 5 | 59 |
Cusp forms | 33 | 5 | 28 |
Eisenstein series | 31 | 0 | 31 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(288))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
288.2.a.a | $1$ | $2.300$ | \(\Q\) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(-4\) | \(0\) | $+$ | $+$ | \(q-4q^{5}-6q^{13}-8q^{17}+11q^{25}+\cdots\) | |
288.2.a.b | $1$ | $2.300$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(-4\) | $-$ | $-$ | \(q-2q^{5}-4q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\) | |
288.2.a.c | $1$ | $2.300$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(4\) | $+$ | $-$ | \(q-2q^{5}+4q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\) | |
288.2.a.d | $1$ | $2.300$ | \(\Q\) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | \(q+2q^{5}+6q^{13}-2q^{17}-q^{25}+10q^{29}+\cdots\) | |
288.2.a.e | $1$ | $2.300$ | \(\Q\) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(4\) | \(0\) | $-$ | $+$ | \(q+4q^{5}-6q^{13}+8q^{17}+11q^{25}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(288))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(288)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)