Defining parameters
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 80 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(400, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 132 | 76 | 56 |
Cusp forms | 108 | 68 | 40 |
Eisenstein series | 24 | 8 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(400, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
400.2.j.a | $2$ | $3.194$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(0\) | \(0\) | \(6\) | \(q+(-1+i)q^{2}-2iq^{3}-2iq^{4}+(2+\cdots)q^{6}+\cdots\) |
400.2.j.b | $8$ | $3.194$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{24}-\zeta_{24}^{5})q^{2}+(\zeta_{24}^{4}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\) |
400.2.j.c | $16$ | $3.194$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{12}q^{2}-\beta _{8}q^{3}+\beta _{15}q^{4}+(-1+\cdots)q^{6}+\cdots\) |
400.2.j.d | $18$ | $3.194$ | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) | None | \(4\) | \(0\) | \(0\) | \(-2\) | \(q-\beta _{7}q^{2}+\beta _{16}q^{3}+\beta _{14}q^{4}+(-1+\cdots)q^{6}+\cdots\) |
400.2.j.e | $24$ | $3.194$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)