Properties

Label 81.5.d
Level $81$
Weight $5$
Character orbit 81.d
Rep. character $\chi_{81}(26,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $30$
Newform subspaces $5$
Sturm bound $45$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 81.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(45\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(81, [\chi])\).

Total New Old
Modular forms 84 34 50
Cusp forms 60 30 30
Eisenstein series 24 4 20

Trace form

\( 30 q + 114 q^{4} - 63 q^{7} + 60 q^{10} + 27 q^{13} - 798 q^{16} + 42 q^{19} + 642 q^{22} + 1671 q^{25} - 5124 q^{28} - 4788 q^{31} - 2232 q^{34} + 3066 q^{37} + 7482 q^{40} + 2682 q^{43} + 22344 q^{46}+ \cdots + 48717 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(81, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
81.5.d.a 81.d 9.d $2$ $8.373$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 27.5.b.a \(0\) \(0\) \(0\) \(-71\) $\mathrm{U}(1)[D_{6}]$ \(q-2^{4}\zeta_{6}q^{4}+(-71+71\zeta_{6})q^{7}+337\zeta_{6}q^{13}+\cdots\)
81.5.d.b 81.d 9.d $4$ $8.373$ \(\Q(\zeta_{12})\) None 27.5.b.c \(0\) \(0\) \(0\) \(38\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta_1 q^{2}-7\beta_{2} q^{4}+(11\beta_{3}-11\beta_1)q^{5}+\cdots\)
81.5.d.c 81.d 9.d $4$ $8.373$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 9.5.b.a \(0\) \(0\) \(0\) \(56\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(7\beta _{1}-7\beta _{3})q^{5}+\cdots\)
81.5.d.d 81.d 9.d $4$ $8.373$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 27.5.b.b \(0\) \(0\) \(0\) \(-34\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+(38+38\beta _{1})q^{4}+(2\beta _{2}-2\beta _{3})q^{5}+\cdots\)
81.5.d.e 81.d 9.d $16$ $8.373$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 81.5.b.b \(0\) \(0\) \(0\) \(-52\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{7}q^{2}+(8-8\beta _{1}-\beta _{4}-\beta _{9})q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(81, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(81, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)