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Properties

Label 36.2.b
Level $36$
Weight $2$
Character orbit 36.b
Rep. character $\chi_{36}(35,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 36.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(36, [\chi])\).

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

Trace form

\( 2q - 4q^{4} + O(q^{10}) \) \( 2q - 4q^{4} + 4q^{10} - 8q^{13} + 8q^{16} + 6q^{25} - 20q^{34} + 4q^{37} - 8q^{40} + 14q^{49} + 16q^{52} + 28q^{58} - 20q^{61} - 16q^{64} - 32q^{73} + 4q^{82} + 20q^{85} + 16q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
36.2.b.a \(2\) \(0.287\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-2q^{4}-\beta q^{5}-2\beta q^{8}+2q^{10}+\cdots\)