Defining parameters
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(48, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 54 | 13 | 41 |
Cusp forms | 42 | 11 | 31 |
Eisenstein series | 12 | 2 | 10 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(48, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
48.7.e.a | $1$ | $11.043$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(27\) | \(0\) | \(286\) | \(q+3^{3}q^{3}+286q^{7}+3^{6}q^{9}+506q^{13}+\cdots\) |
48.7.e.b | $2$ | $11.043$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(-42\) | \(0\) | \(-4\) | \(q+(-21+\beta )q^{3}+10\beta q^{5}-2q^{7}+(153+\cdots)q^{9}+\cdots\) |
48.7.e.c | $2$ | $11.043$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(6\) | \(0\) | \(-484\) | \(q+(3+\beta )q^{3}-6\beta q^{5}-242q^{7}+(-711+\cdots)q^{9}+\cdots\) |
48.7.e.d | $6$ | $11.043$ | 6.0.1173604352.2 | None | \(0\) | \(10\) | \(0\) | \(-156\) | \(q+(2-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-3^{3}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(48, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)