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Properties

Label 3204.1.n
Level $3204$
Weight $1$
Character orbit 3204.n
Rep. character $\chi_{3204}(355,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $3$
Sturm bound $540$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3204 = 2^{2} \cdot 3^{2} \cdot 89 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3204.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3204 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(540\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3204, [\chi])\).

Total New Old
Modular forms 32 32 0
Cusp forms 24 24 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24 q - 12 q^{4} + O(q^{10}) \) \( 24 q - 12 q^{4} - 12 q^{16} - 12 q^{25} - 12 q^{49} + 24 q^{64} + 24 q^{89} - 12 q^{90} + 24 q^{93} - 24 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3204, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3204.1.n.a 3204.n 3204.n $6$ $1.599$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-89}) \) None 3204.1.n.a \(-3\) \(0\) \(0\) \(-3\) \(q-\zeta_{18}^{3}q^{2}-\zeta_{18}^{2}q^{3}+\zeta_{18}^{6}q^{4}+\cdots\)
3204.1.n.b 3204.n 3204.n $6$ $1.599$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-89}) \) None 3204.1.n.a \(-3\) \(0\) \(0\) \(3\) \(q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+\cdots\)
3204.1.n.c 3204.n 3204.n $12$ $1.599$ \(\Q(\zeta_{36})\) $D_{18}$ \(\Q(\sqrt{-89}) \) None 3204.1.n.c \(6\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{6}q^{2}-\zeta_{36}q^{3}+\zeta_{36}^{12}q^{4}+\cdots\)