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Properties

Label 45.10.j
Level $45$
Weight $10$
Character orbit 45.j
Rep. character $\chi_{45}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $104$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
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: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(45, [\chi])\).

Total New Old
Modular forms 112 112 0
Cusp forms 104 104 0
Eisenstein series 8 8 0

Trace form

\( 104 q + 12798 q^{4} + 795 q^{5} + 3516 q^{6} - 35334 q^{9} - 1028 q^{10} - 101718 q^{11} + 241566 q^{14} - 389823 q^{15} - 3013634 q^{16} - 8 q^{19} - 1476798 q^{20} + 1542 q^{21} + 1310430 q^{24} - 730729 q^{25}+ \cdots + 792545166 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.10.j.a 45.j 45.j $104$ $23.177$ None 45.10.j.a \(0\) \(0\) \(795\) \(0\) $\mathrm{SU}(2)[C_{6}]$