Properties

Label 1080.1.i
Level $1080$
Weight $1$
Character orbit 1080.i
Rep. character $\chi_{1080}(269,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $6$
Sturm bound $216$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1080.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(216\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1080, [\chi])\).

Total New Old
Modular forms 30 12 18
Cusp forms 18 12 6
Eisenstein series 12 0 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + 2 q^{4} + O(q^{10}) \) \( 12 q + 2 q^{4} - 4 q^{10} + 6 q^{16} + 2 q^{25} + 4 q^{31} - 10 q^{34} - 2 q^{40} + 2 q^{46} - 10 q^{55} - 4 q^{64} - 6 q^{70} + 6 q^{76} - 4 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1080.1.i.a 1080.i 120.i $1$ $0.539$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-30}) \) None 1080.1.i.a \(-1\) \(0\) \(-1\) \(0\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots\)
1080.1.i.b 1080.i 120.i $1$ $0.539$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-30}) \) None 1080.1.i.a \(-1\) \(0\) \(1\) \(0\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{11}+\cdots\)
1080.1.i.c 1080.i 120.i $1$ $0.539$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-30}) \) None 1080.1.i.a \(1\) \(0\) \(-1\) \(0\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{11}+\cdots\)
1080.1.i.d 1080.i 120.i $1$ $0.539$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-30}) \) None 1080.1.i.a \(1\) \(0\) \(1\) \(0\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots\)
1080.1.i.e 1080.i 120.i $4$ $0.539$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-6}) \) None 1080.1.i.e \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}+(\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1080.1.i.f 1080.i 120.i $4$ $0.539$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-15}) \) None 1080.1.i.f \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1080, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)