Defining parameters
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(400, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 78 | 10 | 68 |
Cusp forms | 42 | 8 | 34 |
Eisenstein series | 36 | 2 | 34 |
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.c.a | $2$ | $3.194$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3 i q^{3}+2 i q^{7}-6 q^{9}-q^{11}+\cdots\) |
400.2.c.b | $2$ | $3.194$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{3}+\beta q^{7}-q^{9}+\beta q^{13}+3\beta q^{17}+\cdots\) |
400.2.c.c | $2$ | $3.194$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+i q^{3}-2 i q^{7}+2 q^{9}+3 q^{11}+\cdots\) |
400.2.c.d | $2$ | $3.194$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2\beta q^{7}+3 q^{9}-4 q^{11}+\beta q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)