↑

Properties

Label 3240.1.z
Level $3240$
Weight $1$
Character orbit 3240.z
Rep. character $\chi_{3240}(379,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $12$
Sturm bound $648$
Trace bound $10$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3240.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 12 \)
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

\( 28 q - 8 q^{4} + O(q^{10}) \) \( 28 q - 8 q^{4} - 8 q^{16} - 14 q^{25} + 6 q^{34} + 6 q^{40} - 12 q^{46} - 2 q^{49} + 28 q^{64} + 6 q^{76} - 16 q^{91} + 8 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.z.a 3240.z 360.z $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-15}) \) None 1080.1.p.a \(-2\) \(0\) \(-1\) \(0\) \(q-q^{2}+q^{4}+\zeta_{6}^{2}q^{5}-q^{8}-\zeta_{6}^{2}q^{10}+\cdots\)
3240.1.z.b 3240.z 360.z $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.a \(-1\) \(0\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
3240.1.z.c 3240.z 360.z $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.a \(-1\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)
3240.1.z.d 3240.z 360.z $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{6}) \) 360.1.p.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.z.e 3240.z 360.z $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-15}) \) None 1080.1.p.a \(-1\) \(0\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots\)
3240.1.z.f 3240.z 360.z $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{6}) \) 360.1.p.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.z.g 3240.z 360.z $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-15}) \) None 1080.1.p.a \(1\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots\)
3240.1.z.h 3240.z 360.z $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.a \(1\) \(0\) \(1\) \(-1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
3240.1.z.i 3240.z 360.z $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.a \(1\) \(0\) \(1\) \(1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)
3240.1.z.j 3240.z 360.z $2$ $1.617$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-15}) \) None 1080.1.p.a \(2\) \(0\) \(1\) \(0\) \(q+q^{2}+q^{4}-\zeta_{6}^{2}q^{5}+q^{8}-\zeta_{6}^{2}q^{10}+\cdots\)
3240.1.z.k 3240.z 360.z $4$ $1.617$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.e \(-2\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{5}+\cdots\)
3240.1.z.l 3240.z 360.z $4$ $1.617$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-10}) \) None 3240.1.p.e \(2\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)