Defining parameters
Level: | \( N \) | \(=\) | \( 272 = 2^{4} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 272.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(272, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 114 | 28 | 86 |
Cusp forms | 102 | 26 | 76 |
Eisenstein series | 12 | 2 | 10 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(272, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
272.4.b.a | $2$ | $16.049$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2\beta q^{3}-\beta q^{5}-3\beta q^{7}-5q^{9}-20\beta q^{11}+\cdots\) |
272.4.b.b | $2$ | $16.049$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}-4iq^{5}+17iq^{7}+23q^{9}+\cdots\) |
272.4.b.c | $4$ | $16.049$ | 4.0.1499912.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-15+\cdots)q^{9}+\cdots\) |
272.4.b.d | $4$ | $16.049$ | 4.0.4669632.2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\) |
272.4.b.e | $6$ | $16.049$ | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\) |
272.4.b.f | $8$ | $16.049$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}+\beta _{4}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(272, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(272, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)