Properties

Label 45.2.b
Level $45$
Weight $2$
Character orbit 45.b
Rep. character $\chi_{45}(19,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(45, [\chi])\).

Total New Old
Modular forms 10 4 6
Cusp forms 2 2 0
Eisenstein series 8 2 6

Trace form

\( 2 q - 6 q^{4} + O(q^{10}) \) \( 2 q - 6 q^{4} + 10 q^{10} - 2 q^{16} - 8 q^{19} - 10 q^{25} + 16 q^{31} + 20 q^{34} - 10 q^{40} - 40 q^{46} + 14 q^{49} + 4 q^{61} + 26 q^{64} + 24 q^{76} - 32 q^{79} - 20 q^{85} - 40 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.2.b.a 45.b 5.b $2$ $0.359$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) 45.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}-3q^{4}-\beta q^{5}-\beta q^{8}+5q^{10}+\cdots\)