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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
81.2.c.a \(2\) \(0.647\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\cdots\)
81.2.c.b \(4\) \(0.647\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)