Defining parameters
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(54\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(108, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 45 | 3 | 42 |
Cusp forms | 27 | 3 | 24 |
Eisenstein series | 18 | 0 | 18 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(108, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
108.3.c.a | $1$ | $2.943$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(11\) | \(q+11q^{7}+23q^{13}-37q^{19}+5^{2}q^{25}+\cdots\) |
108.3.c.b | $2$ | $2.943$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(-14\) | \(q+iq^{5}-7q^{7}+iq^{11}+14q^{13}+2iq^{17}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(108, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)