Defining parameters
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(224, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 12 | 60 |
Cusp forms | 56 | 12 | 44 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(224, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
224.3.d.a | $4$ | $6.104$ | \(\Q(i, \sqrt{7})\) | None | \(0\) | \(0\) | \(-8\) | \(0\) | \(q+\beta _{1}q^{3}+(-2+\beta _{2})q^{5}-\beta _{3}q^{7}+5q^{9}+\cdots\) |
224.3.d.b | $8$ | $6.104$ | 8.0.1997017344.2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}-\beta _{4}q^{5}-\beta _{3}q^{7}+(-5+\beta _{2}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(224, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)