Defining parameters
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(14\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(49, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 8 | 6 |
Cusp forms | 6 | 4 | 2 |
Eisenstein series | 8 | 4 | 4 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(49, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
49.3.b.a | $4$ | $1.335$ | 4.0.2048.2 | None | \(4\) | \(0\) | \(0\) | \(0\) | \(q+(1+\beta _{2})q^{2}-\beta _{3}q^{3}+(-1+2\beta _{2}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(49, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(49, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)