Defining parameters
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(735, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 128 | 52 | 76 |
Cusp forms | 96 | 52 | 44 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(735, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
735.2.b.a | $2$ | $5.869$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-3\) | \(-2\) | \(0\) | \(q+(1-2\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-q^{4}+\cdots\) |
735.2.b.b | $2$ | $5.869$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(3\) | \(2\) | \(0\) | \(q+(1-2\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-q^{4}+q^{5}+\cdots\) |
735.2.b.c | $8$ | $5.869$ | 8.0.856615824.2 | None | \(0\) | \(-1\) | \(8\) | \(0\) | \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+q^{5}+\cdots\) |
735.2.b.d | $8$ | $5.869$ | 8.0.856615824.2 | None | \(0\) | \(1\) | \(-8\) | \(0\) | \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots\) |
735.2.b.e | $16$ | $5.869$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(-4\) | \(16\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\) |
735.2.b.f | $16$ | $5.869$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(4\) | \(-16\) | \(0\) | \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(735, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)