Properties

Label 1296.1.o
Level $1296$
Weight $1$
Character orbit 1296.o
Rep. character $\chi_{1296}(271,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $10$
Newform subspaces $4$
Sturm bound $216$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1296.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(216\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1296, [\chi])\).

Total New Old
Modular forms 94 10 84
Cusp forms 22 10 12
Eisenstein series 72 0 72

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10 q + O(q^{10}) \) \( 10 q - 2 q^{13} - q^{25} - 4 q^{37} + q^{49} + 2 q^{61} + 4 q^{73} + 6 q^{85} + 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1296, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1296.1.o.a 1296.o 36.f $2$ $0.647$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-3\) \(q+(-1+\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1296.1.o.b 1296.o 36.f $2$ $0.647$ \(\Q(\sqrt{-3}) \) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{25}+q^{37}+\zeta_{6}^{2}q^{49}+\cdots\)
1296.1.o.c 1296.o 36.f $2$ $0.647$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(3\) \(q+(1-\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1296.1.o.d 1296.o 36.f $4$ $0.647$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{5}-\zeta_{12}^{2}q^{13}+(\zeta_{12}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)