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Properties

Label 39.5.h
Level $39$
Weight $5$
Character orbit 39.h
Rep. character $\chi_{39}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $34$
Newform subspaces $2$
Sturm bound $23$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 39.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(23\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(39, [\chi])\).

Total New Old
Modular forms 42 42 0
Cusp forms 34 34 0
Eisenstein series 8 8 0

Trace form

\( 34 q - q^{3} - 130 q^{4} - 102 q^{6} - 93 q^{7} - 35 q^{9} + 18 q^{10} + 220 q^{12} + 233 q^{13} - 96 q^{15} - 1070 q^{16} + 792 q^{19} + 180 q^{22} + 2514 q^{24} + 1874 q^{25} + 302 q^{27} - 300 q^{28}+ \cdots + 9183 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(39, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
39.5.h.a 39.h 39.h $2$ $4.031$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 39.5.h.a \(0\) \(9\) \(0\) \(117\) $\mathrm{U}(1)[D_{6}]$ \(q+(9-9\zeta_{6})q^{3}+2^{4}\zeta_{6}q^{4}+(78-39\zeta_{6})q^{7}+\cdots\)
39.5.h.b 39.h 39.h $32$ $4.031$ None 39.5.h.b \(0\) \(-10\) \(0\) \(-210\) $\mathrm{SU}(2)[C_{6}]$