Defining parameters
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.s (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 80 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 528 | 76 | 452 |
Cusp forms | 432 | 68 | 364 |
Eisenstein series | 96 | 8 | 88 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1600.2.s.a | $2$ | $12.776$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-4\) | \(0\) | \(-6\) | \(q-2 q^{3}+(-3 i-3)q^{7}+q^{9}+(-i+1)q^{11}+\cdots\) |
1600.2.s.b | $8$ | $12.776$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta_{7}+\beta_{5}+\beta_1)q^{3}+(-\beta_{7}+2\beta_{5}+\cdots-\beta_1)q^{7}+\cdots\) |
1600.2.s.c | $16$ | $12.776$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{4}q^{3}-\beta _{7}q^{7}+(1-\beta _{12})q^{9}+(-1+\cdots)q^{11}+\cdots\) |
1600.2.s.d | $18$ | $12.776$ | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q+\beta _{1}q^{3}+\beta _{11}q^{7}+(1+\beta _{3})q^{9}+(-\beta _{13}+\cdots)q^{11}+\cdots\) |
1600.2.s.e | $24$ | $12.776$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)