Properties

Label 81.2.c
Level $81$
Weight $2$
Character orbit 81.c
Rep. character $\chi_{81}(28,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $2$
Sturm bound $18$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 81.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(81, [\chi])\).

Total New Old
Modular forms 30 10 20
Cusp forms 6 6 0
Eisenstein series 24 4 20

Trace form

\( 6 q - 3 q^{7} + O(q^{10}) \) \( 6 q - 3 q^{7} - 12 q^{10} - 3 q^{13} + 6 q^{16} - 6 q^{19} + 12 q^{22} + 9 q^{25} + 12 q^{28} - 12 q^{31} - 18 q^{34} - 6 q^{37} - 6 q^{40} - 12 q^{43} + 24 q^{46} + 12 q^{49} + 12 q^{52} + 24 q^{55} - 6 q^{58} + 15 q^{61} - 12 q^{64} + 15 q^{67} + 12 q^{70} - 42 q^{73} - 18 q^{76} - 21 q^{79} - 48 q^{82} + 18 q^{85} - 12 q^{88} - 18 q^{91} - 24 q^{94} + 15 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(81, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
81.2.c.a 81.c 9.c $2$ $0.647$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 27.2.a.a \(0\) \(0\) \(0\) \(1\) $\mathrm{U}(1)[D_{3}]$ \(q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\cdots\)
81.2.c.b 81.c 9.c $4$ $0.647$ \(\Q(\zeta_{12})\) None 81.2.a.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)