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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
45.2.b.a \(2\) \(0.359\) \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-3q^{4}-\beta q^{5}-\beta q^{8}+5q^{10}+\cdots\)