Properties

Label 3360.1.ds
Level $3360$
Weight $1$
Character orbit 3360.ds
Rep. character $\chi_{3360}(1409,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $2$
Sturm bound $768$
Trace bound $21$

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Defining parameters

Level: \( N \) \(=\) \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3360.ds (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(768\)
Trace bound: \(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3360, [\chi])\).

Total New Old
Modular forms 80 16 64
Cusp forms 16 16 0
Eisenstein series 64 0 64

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16q + O(q^{10}) \) \( 16q - 4q^{21} + 8q^{25} - 4q^{45} - 16q^{69} - 4q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3360, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3360.1.ds.a \(8\) \(1.677\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{3}+\zeta_{24}^{2}q^{5}+\zeta_{24}^{7}q^{7}+\cdots\)
3360.1.ds.b \(8\) \(1.677\) \(\Q(\zeta_{24})\) \(D_{12}\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{2}q^{5}-\zeta_{24}q^{7}+\zeta_{24}^{10}q^{9}+\cdots\)