Properties

Label 156.1.s
Level $156$
Weight $1$
Character orbit 156.s
Rep. character $\chi_{156}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $28$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 156.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(156, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

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

\( 2q + q^{3} - 3q^{7} - q^{9} + O(q^{10}) \) \( 2q + q^{3} - 3q^{7} - q^{9} + q^{13} - 2q^{25} - 2q^{27} + 2q^{39} + q^{43} + 2q^{49} - q^{61} + 3q^{63} + 3q^{67} - q^{75} + 2q^{79} - q^{81} - 3q^{91} - 3q^{93} - 3q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(156, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
156.1.s.a \(2\) \(0.078\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-3\) \(q+\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)