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Properties

Label 45.10.l
Level $45$
Weight $10$
Character orbit 45.l
Rep. character $\chi_{45}(2,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $208$
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.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
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 224 224 0
Cusp forms 208 208 0
Eisenstein series 16 16 0

Trace form

\( 208 q - 6 q^{2} + 144 q^{3} - 6 q^{5} - 9096 q^{6} - 2 q^{7} - 8 q^{10} - 92484 q^{11} - 191946 q^{12} - 2 q^{13} + 40224 q^{15} + 6029308 q^{16} + 1163616 q^{18} + 4890618 q^{20} - 592224 q^{21} - 2050 q^{22}+ \cdots - 2939132522 q^{97}+O(q^{100}) \) 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.l.a 45.l 45.l $208$ $23.177$ None 45.10.l.a \(-6\) \(144\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{12}]$