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Properties

Label 45.6.j
Level $45$
Weight $6$
Character orbit 45.j
Rep. character $\chi_{45}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 45.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(45, [\chi])\).

Total New Old
Modular forms 64 64 0
Cusp forms 56 56 0
Eisenstein series 8 8 0

Trace form

\( 56 q + 414 q^{4} - 30 q^{5} + 12 q^{6} + 468 q^{9} - 68 q^{10} - 780 q^{11} + 1398 q^{14} + 672 q^{15} - 5570 q^{16} - 8 q^{19} + 3522 q^{20} - 4848 q^{21} - 7554 q^{24} - 1654 q^{25} + 16968 q^{26} + 2700 q^{29}+ \cdots + 1001340 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.6.j.a 45.j 45.j $56$ $7.217$ None 45.6.j.a \(0\) \(0\) \(-30\) \(0\) $\mathrm{SU}(2)[C_{6}]$