Defining parameters
Level: | \( N \) | \(=\) | \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1872.n (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 156 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1344\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1872, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1032 | 84 | 948 |
Cusp forms | 984 | 84 | 900 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1872.4.n.a | $4$ | $110.452$ | \(\Q(\sqrt{-2}, \sqrt{13})\) | \(\Q(\sqrt{-13}) \) | \(0\) | \(0\) | \(0\) | \(-76\) | \(q+(-19+5\beta _{1})q^{7}+(5\beta _{2}+5\beta _{3})q^{11}+\cdots\) |
1872.4.n.b | $4$ | $110.452$ | \(\Q(\zeta_{8})\) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{3}q^{5}+(-46-\zeta_{8})q^{13}+5\zeta_{8}^{2}q^{17}+\cdots\) |
1872.4.n.c | $4$ | $110.452$ | \(\Q(\sqrt{-2}, \sqrt{13})\) | \(\Q(\sqrt{-13}) \) | \(0\) | \(0\) | \(0\) | \(76\) | \(q+(19-5\beta _{1})q^{7}+(5\beta _{2}+5\beta _{3})q^{11}+\cdots\) |
1872.4.n.d | $16$ | $110.452$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{5}+\beta _{10}q^{7}+\beta _{4}q^{11}+(11-\beta _{11}+\cdots)q^{13}+\cdots\) |
1872.4.n.e | $56$ | $110.452$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{4}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)