Properties

Label 936.1.o
Level $936$
Weight $1$
Character orbit 936.o
Rep. character $\chi_{936}(883,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $3$
Sturm bound $168$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 936.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(168\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(936, [\chi])\).

Total New Old
Modular forms 20 8 12
Cusp forms 12 6 6
Eisenstein series 8 2 6

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q + 2 q^{4} + O(q^{10}) \) \( 6 q + 2 q^{4} - 6 q^{10} + 2 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{22} + 4 q^{25} - 2 q^{26} - 2 q^{35} + 2 q^{40} + 6 q^{43} - 4 q^{49} - 4 q^{52} + 2 q^{56} - 4 q^{62} + 2 q^{64} + 2 q^{65} + 2 q^{68} + 2 q^{74} + 4 q^{82} - 4 q^{88} - 2 q^{91} + 2 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(936, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
936.1.o.a 936.o 104.h $1$ $0.467$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(-1\) \(0\) \(1\) \(-1\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
936.1.o.b 936.o 104.h $1$ $0.467$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
936.1.o.c 936.o 104.h $4$ $0.467$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(936, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(936, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)