Properties

Label 2760.1.bv
Level $2760$
Weight $1$
Character orbit 2760.bv
Rep. character $\chi_{2760}(137,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $2$
Sturm bound $576$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2760.bv (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 345 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2760, [\chi])\).

Total New Old
Modular forms 40 8 32
Cusp forms 8 8 0
Eisenstein series 32 0 32

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 8 0

Trace form

\( 8 q + 4 q^{3} + O(q^{10}) \) \( 8 q + 4 q^{3} + 8 q^{13} + 4 q^{27} - 8 q^{31} - 4 q^{75} + 8 q^{81} + 8 q^{85} - 4 q^{87} - 4 q^{93} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2760, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2760.1.bv.a 2760.bv 345.l $4$ $1.377$ \(\Q(\zeta_{8})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{3}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
2760.1.bv.b 2760.bv 345.l $4$ $1.377$ \(\Q(\zeta_{8})\) $S_{4}$ None None \(0\) \(4\) \(0\) \(0\) \(q+q^{3}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{3}q^{7}+q^{9}+(1+\cdots)q^{13}+\cdots\)