Properties

Label 3360.1.bn
Level $3360$
Weight $1$
Character orbit 3360.bn
Rep. character $\chi_{3360}(1217,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $16$
Newform subspaces $4$
Sturm bound $768$
Trace bound $23$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3360.bn (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
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 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

\( 16 q + O(q^{10}) \) \( 16 q - 16 q^{81} - 16 q^{93} + O(q^{100}) \)

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.bn.a $4$ $1.677$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
3360.1.bn.b $4$ $1.677$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
3360.1.bn.c $4$ $1.677$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
3360.1.bn.d $4$ $1.677$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)