Properties

Label 2760.1.cm
Level $2760$
Weight $1$
Character orbit 2760.cm
Rep. character $\chi_{2760}(29,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $80$
Newform subspaces $6$
Sturm bound $576$
Trace bound $34$

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Defining parameters

Level: \( N \) \(=\) \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2760.cm (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2760 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 6 \)
Sturm bound: \(576\)
Trace bound: \(34\)

Dimensions

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

Total New Old
Modular forms 160 160 0
Cusp forms 80 80 0
Eisenstein series 80 80 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 80 0 0 0

Trace form

\( 80 q + 4 q^{6} + O(q^{10}) \) \( 80 q + 4 q^{6} - 4 q^{10} - 4 q^{15} - 8 q^{16} - 4 q^{24} - 4 q^{30} + 14 q^{34} - 8 q^{36} + 36 q^{39} - 18 q^{40} - 4 q^{46} - 8 q^{49} + 18 q^{54} + 36 q^{55} - 18 q^{60} - 8 q^{66} - 16 q^{79} - 8 q^{81} + 4 q^{90} - 8 q^{94} + 4 q^{96} + O(q^{100}) \)

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.cm.a 2760.cm 2760.bm $10$ $1.377$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-30}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q+\zeta_{22}^{8}q^{2}-\zeta_{22}^{9}q^{3}-\zeta_{22}^{5}q^{4}+\cdots\)
2760.1.cm.b 2760.cm 2760.bm $10$ $1.377$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-30}) \) None \(-1\) \(1\) \(1\) \(0\) \(q+\zeta_{22}^{8}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}^{5}q^{4}+\cdots\)
2760.1.cm.c 2760.cm 2760.bm $10$ $1.377$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-30}) \) None \(1\) \(-1\) \(1\) \(0\) \(q-\zeta_{22}^{8}q^{2}-\zeta_{22}^{9}q^{3}-\zeta_{22}^{5}q^{4}+\cdots\)
2760.1.cm.d 2760.cm 2760.bm $10$ $1.377$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-30}) \) None \(1\) \(1\) \(-1\) \(0\) \(q-\zeta_{22}^{8}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}^{5}q^{4}+\cdots\)
2760.1.cm.e 2760.cm 2760.bm $20$ $1.377$ \(\Q(\zeta_{44})\) $D_{22}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{44}^{3}q^{2}+\zeta_{44}^{21}q^{3}+\zeta_{44}^{6}q^{4}+\cdots\)
2760.1.cm.f 2760.cm 2760.bm $20$ $1.377$ \(\Q(\zeta_{44})\) $D_{22}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{44}^{5}q^{2}-\zeta_{44}^{21}q^{3}+\zeta_{44}^{10}q^{4}+\cdots\)