Defining parameters
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(80\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(128, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 16 | 56 |
Cusp forms | 56 | 16 | 40 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(128, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
128.5.c.a | $8$ | $13.231$ | 8.0.205520896.4 | None | \(0\) | \(0\) | \(-48\) | \(0\) | \(q+\beta _{1}q^{3}+(-6-\beta _{2})q^{5}+(-\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\) |
128.5.c.b | $8$ | $13.231$ | 8.0.205520896.4 | None | \(0\) | \(0\) | \(48\) | \(0\) | \(q+\beta _{1}q^{3}+(6+\beta _{2})q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(128, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)