Properties

Label 3360.1.cv
Level $3360$
Weight $1$
Character orbit 3360.cv
Rep. character $\chi_{3360}(1553,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $4$
Sturm bound $768$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3360.cv (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 840 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(768\)
Trace bound: \(23\)

Dimensions

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

Total New Old
Modular forms 160 40 120
Cusp forms 96 24 72
Eisenstein series 64 16 48

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

\( 24q + 4q^{7} + O(q^{10}) \) \( 24q + 4q^{7} - 8q^{15} + 8q^{57} + 4q^{63} - 8q^{81} + O(q^{100}) \)

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.cv.a \(4\) \(1.677\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{3}-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
3360.1.cv.b \(4\) \(1.677\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{3}q^{3}-\zeta_{8}q^{5}+q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
3360.1.cv.c \(8\) \(1.677\) \(\Q(\zeta_{16})\) \(D_{8}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{3}-\zeta_{16}q^{5}-\zeta_{16}^{6}q^{7}+\zeta_{16}^{2}q^{9}+\cdots\)
3360.1.cv.d \(8\) \(1.677\) \(\Q(\zeta_{16})\) \(D_{8}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{3}q^{3}+\zeta_{16}q^{5}-\zeta_{16}^{6}q^{7}+\zeta_{16}^{6}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3360, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 3}\)