Properties

Label 72.2.l
Level $72$
Weight $2$
Character orbit 72.l
Rep. character $\chi_{72}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 72.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(72, [\chi])\).

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20 q - 3 q^{2} - 4 q^{3} - q^{4} - 7 q^{6} - 4 q^{9} - 6 q^{11} + 2 q^{12} - 18 q^{14} - q^{16} - 16 q^{18} - 8 q^{19} + 18 q^{20} - 5 q^{22} + 29 q^{24} - 4 q^{25} - 16 q^{27} - 12 q^{28} + 12 q^{30}+ \cdots + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.2.l.a 72.l 72.l $4$ $0.575$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) 72.2.l.a \(0\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
72.2.l.b 72.l 72.l $16$ $0.575$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 72.2.l.b \(-3\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)