Properties

Label 3456.1.n
Level $3456$
Weight $1$
Character orbit 3456.n
Rep. character $\chi_{3456}(449,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $576$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 3456 = 2^{7} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3456.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3456, [\chi])\).

Total New Old
Modular forms 132 4 128
Cusp forms 36 4 32
Eisenstein series 96 0 96

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + O(q^{10}) \) \( 4 q + 2 q^{25} + 6 q^{41} + 2 q^{49} + 4 q^{73} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3456, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3456.1.n.a 3456.n 72.j $2$ $1.725$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{11}+(-\zeta_{6}-\zeta_{6}^{2})q^{17}+(-\zeta_{6}+\cdots)q^{19}+\cdots\)
3456.1.n.b 3456.n 72.j $2$ $1.725$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{11}+(-\zeta_{6}-\zeta_{6}^{2})q^{17}+(\zeta_{6}+\cdots)q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3456, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3456, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1728, [\chi])\)\(^{\oplus 2}\)