Properties

Label 2775.1.x
Level $2775$
Weight $1$
Character orbit 2775.x
Rep. character $\chi_{2775}(824,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $380$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2775 = 3 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2775.x (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(380\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2775, [\chi])\).

Total New Old
Modular forms 28 12 16
Cusp forms 4 4 0
Eisenstein series 24 8 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + 2 q^{4} + 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{4} + 2 q^{9} - 2 q^{16} + 4 q^{19} + 2 q^{21} - 4 q^{31} + 4 q^{36} - 2 q^{39} - 4 q^{61} - 4 q^{64} - 4 q^{76} - 2 q^{79} - 2 q^{81} + 4 q^{84} - 2 q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2775, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2775.1.x.a \(4\) \(1.385\) \(\Q(\zeta_{12})\) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{7}+\cdots\)