Properties

Label 31.1.b
Level $31$
Weight $1$
Character orbit 31.b
Rep. character $\chi_{31}(30,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $2$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 31.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(31, [\chi])\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 0
Eisenstein series 1 1 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{2} - q^{5} - q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{5} - q^{7} + q^{8} + q^{9} + q^{10} + q^{14} - q^{16} - q^{18} - q^{19} + q^{31} + q^{35} + q^{38} - q^{40} - q^{41} - q^{45} + 2 q^{47} - q^{56} - q^{59} - q^{62} - q^{63} + q^{64} + 2 q^{67} - q^{70} - q^{71} + q^{72} + q^{80} + q^{81} + q^{82} + q^{90} - 2 q^{94} + q^{95} - q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(31, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
31.1.b.a $1$ $0.015$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-31}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)