Properties

Label 120.1.i
Level $120$
Weight $1$
Character orbit 120.i
Rep. character $\chi_{120}(29,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 120.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(120, [\chi])\).

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

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} + 2 q^{10} + 2 q^{15} + 2 q^{16} + 2 q^{24} - 2 q^{25} - 4 q^{31} + 2 q^{36} - 2 q^{40} + 2 q^{49} + 2 q^{54} - 2 q^{60} - 2 q^{64} + 4 q^{79} + 2 q^{81} - 2 q^{90} - 2 q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(120, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
120.1.i.a 120.i 120.i $2$ $0.060$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}+iq^{5}-q^{6}+iq^{8}+\cdots\)