Defining parameters
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.m (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(1344\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4004, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 684 | 68 | 616 |
Cusp forms | 660 | 68 | 592 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(4004, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
4004.2.m.a | $2$ | $31.972$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q+2q^{3}+iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\) |
4004.2.m.b | $30$ | $31.972$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
4004.2.m.c | $36$ | $31.972$ | None | \(0\) | \(-4\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(4004, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4004, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(572, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1001, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2002, [\chi])\)\(^{\oplus 2}\)