Defining parameters
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(700, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 138 | 8 | 130 |
Cusp forms | 102 | 8 | 94 |
Eisenstein series | 36 | 0 | 36 |
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.e.a | $2$ | $5.590$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3iq^{3}+iq^{7}-6q^{9}-5q^{11}-3iq^{13}+\cdots\) |
700.2.e.b | $2$ | $5.590$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2iq^{3}+iq^{7}-q^{9}+3q^{11}+4iq^{13}+\cdots\) |
700.2.e.c | $2$ | $5.590$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}-iq^{7}+2q^{9}+3q^{11}-iq^{13}+\cdots\) |
700.2.e.d | $2$ | $5.590$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{7}+3q^{9}-5q^{11}-6iq^{13}-4iq^{17}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(700, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)