Defining parameters
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(252\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{21}(72, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 244 | 101 | 143 |
Cusp forms | 236 | 99 | 137 |
Eisenstein series | 8 | 2 | 6 |
Trace form
Decomposition of \(S_{21}^{\mathrm{new}}(72, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
72.21.b.a | $1$ | $182.530$ | \(\Q\) | \(\Q(\sqrt{-2}) \) | \(-1024\) | \(0\) | \(0\) | \(0\) | \(q-2^{10}q^{2}+2^{20}q^{4}-2^{30}q^{8}+42383023726q^{11}+\cdots\) |
72.21.b.b | $18$ | $182.530$ | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) | None | \(398\) | \(0\) | \(0\) | \(0\) | \(q+(22+\beta _{1})q^{2}+(40275+21\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\) |
72.21.b.c | $40$ | $182.530$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
72.21.b.d | $40$ | $182.530$ | None | \(1254\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{21}^{\mathrm{old}}(72, [\chi])\) into lower level spaces
\( S_{21}^{\mathrm{old}}(72, [\chi]) \simeq \) \(S_{21}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)