Defining parameters
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.be (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 140 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(700, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 528 | 304 | 224 |
Cusp forms | 432 | 272 | 160 |
Eisenstein series | 96 | 32 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(700, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
700.2.be.a | $8$ | $5.590$ | 8.0.12960000.1 | \(\Q(\sqrt{-5}) \) | \(-4\) | \(2\) | \(0\) | \(6\) | \(q+(\beta _{1}-\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots\) |
700.2.be.b | $8$ | $5.590$ | 8.0.12960000.1 | \(\Q(\sqrt{-5}) \) | \(4\) | \(-2\) | \(0\) | \(-6\) | \(q+(1-\beta _{4}-\beta _{7})q^{2}+(-1-\beta _{3}+2\beta _{6}+\cdots)q^{3}+\cdots\) |
700.2.be.c | $8$ | $5.590$ | 8.0.\(\cdots\).9 | None | \(4\) | \(0\) | \(0\) | \(0\) | \(q+(1-\beta _{2}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-2\beta _{2}+\cdots)q^{4}+\cdots\) |
700.2.be.d | $48$ | $5.590$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
700.2.be.e | $72$ | $5.590$ | None | \(-2\) | \(0\) | \(0\) | \(0\) | ||
700.2.be.f | $128$ | $5.590$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(700, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)