Properties

Label 81.5.b
Level $81$
Weight $5$
Character orbit 81.b
Rep. character $\chi_{81}(80,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $2$
Sturm bound $45$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 81.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(45\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 42 18 24
Cusp forms 30 14 16
Eisenstein series 12 4 8

Trace form

\( 14 q - 94 q^{4} + 28 q^{7} + 156 q^{10} - 248 q^{13} + 110 q^{16} - 566 q^{19} + 1878 q^{22} - 1126 q^{25} - 944 q^{28} + 364 q^{31} + 2502 q^{34} + 4600 q^{37} - 8580 q^{40} - 3266 q^{43} - 2364 q^{46}+ \cdots + 30430 q^{97}+O(q^{100}) \) 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.b.a 81.b 3.b $6$ $8.373$ 6.0.39400128.1 None 9.5.d.a \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-5+\beta _{2})q^{4}+\beta _{4}q^{5}+(-4+\cdots)q^{7}+\cdots\)
81.5.b.b 81.b 3.b $8$ $8.373$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 81.5.b.b \(0\) \(0\) \(0\) \(52\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-8+\beta _{5})q^{4}+(\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)

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

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