Properties

Label 2888.1.f
Level $2888$
Weight $1$
Character orbit 2888.f
Rep. character $\chi_{2888}(723,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $380$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2888.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(380\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2888, [\chi])\).

Total New Old
Modular forms 28 25 3
Cusp forms 8 8 0
Eisenstein series 20 17 3

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

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

Trace form

\( 8 q + 8 q^{4} - 2 q^{6} + 6 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{4} - 2 q^{6} + 6 q^{9} - 2 q^{11} + 8 q^{16} - 2 q^{17} - 2 q^{24} + 8 q^{25} + 6 q^{36} - 2 q^{43} - 2 q^{44} + 8 q^{49} - 4 q^{54} + 8 q^{64} - 4 q^{66} - 2 q^{68} - 2 q^{73} + 4 q^{81} - 2 q^{82} - 2 q^{83} - 2 q^{96} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2888, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2888.1.f.a 2888.f 8.d $1$ $1.441$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots\)
2888.1.f.b 2888.f 8.d $1$ $1.441$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots\)
2888.1.f.c 2888.f 8.d $3$ $1.441$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-2}) \) None \(-3\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-q^{8}+\cdots\)
2888.1.f.d 2888.f 8.d $3$ $1.441$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-2}) \) None \(3\) \(0\) \(0\) \(0\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{8}+\cdots\)