Properties

Label 216.2.l
Level $216$
Weight $2$
Character orbit 216.l
Rep. character $\chi_{216}(35,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(216, [\chi])\).

Total New Old
Modular forms 84 28 56
Cusp forms 60 20 40
Eisenstein series 24 8 16

Trace form

\( 20 q + 3 q^{2} - q^{4} + O(q^{10}) \) \( 20 q + 3 q^{2} - q^{4} + 6 q^{11} + 18 q^{14} - q^{16} - 8 q^{19} - 18 q^{20} - 5 q^{22} - 4 q^{25} - 12 q^{28} - 27 q^{32} - 5 q^{34} - 21 q^{38} - 12 q^{40} + 18 q^{41} - 2 q^{43} + 12 q^{46} - 4 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 30 q^{59} + 2 q^{64} + 6 q^{65} - 2 q^{67} + 45 q^{68} + 18 q^{70} - 8 q^{73} + 60 q^{74} - 11 q^{76} + 10 q^{82} - 54 q^{83} + 87 q^{86} - 5 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
216.2.l.a \(4\) \(1.725\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+2\beta _{3}q^{8}+(3-\beta _{1}+\cdots)q^{11}+\cdots\)
216.2.l.b \(16\) \(1.725\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(3\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{2}+(-1-\beta _{1}+\beta _{2}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(216, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)