Properties

Label 3240.1.bh
Level $3240$
Weight $1$
Character orbit 3240.bh
Rep. character $\chi_{3240}(269,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $9$
Sturm bound $648$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3240.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 9 \)
Sturm bound: \(648\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3240, [\chi])\).

Total New Old
Modular forms 76 36 40
Cusp forms 28 28 0
Eisenstein series 48 8 40

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 28 0 0 0

Trace form

\( 28 q + O(q^{10}) \) \( 28 q - 4 q^{10} - 8 q^{16} + 10 q^{34} + 4 q^{40} + 4 q^{46} - 2 q^{49} - 20 q^{55} - 12 q^{64} + 6 q^{70} - 6 q^{76} - 4 q^{79} + 4 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3240, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3240.1.bh.a 3240.bh 360.ah $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-30}) \) None 1080.1.i.a \(-1\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+q^{8}+\cdots\)
3240.1.bh.b 3240.bh 360.ah $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-30}) \) None 1080.1.i.a \(-1\) \(0\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots\)
3240.1.bh.c 3240.bh 360.ah $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-30}) \) None 1080.1.i.a \(1\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots\)
3240.1.bh.d 3240.bh 360.ah $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-30}) \) None 1080.1.i.a \(1\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-q^{8}+\cdots\)
3240.1.bh.e 3240.bh 360.ah $4$ $1.617$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-15}) \) None 1080.1.i.f \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
3240.1.bh.f 3240.bh 360.ah $4$ $1.617$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-6}) \) None 1080.1.i.e \(0\) \(0\) \(0\) \(-6\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
3240.1.bh.g 3240.bh 360.ah $4$ $1.617$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-15}) \) None 1080.1.i.f \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots\)
3240.1.bh.h 3240.bh 360.ah $4$ $1.617$ \(\Q(\zeta_{12})\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) 120.1.i.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
3240.1.bh.i 3240.bh 360.ah $4$ $1.617$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-6}) \) None 1080.1.i.e \(0\) \(0\) \(0\) \(6\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}+(1+\cdots)q^{7}+\cdots\)