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Properties

Label 2888.1.k
Level $2888$
Weight $1$
Character orbit 2888.k
Rep. character $\chi_{2888}(2595,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $14$
Newform subspaces $3$
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.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
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 58 46 12
Cusp forms 18 14 4
Eisenstein series 40 32 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 0 0

Trace form

\( 14 q + q^{2} - q^{3} - 7 q^{4} + q^{6} - 2 q^{8} - 6 q^{9} + O(q^{10}) \) \( 14 q + q^{2} - q^{3} - 7 q^{4} + q^{6} - 2 q^{8} - 6 q^{9} - 2 q^{11} + 2 q^{12} - 7 q^{16} + 4 q^{17} - q^{22} + q^{24} - 7 q^{25} - 2 q^{27} + q^{32} + q^{33} + 2 q^{34} - 6 q^{36} - q^{41} + 4 q^{43} + q^{44} - q^{48} + 14 q^{49} - 2 q^{50} - 2 q^{51} + 5 q^{54} - q^{59} + 14 q^{64} + 5 q^{66} - q^{67} - 8 q^{68} + q^{73} + 2 q^{75} - 5 q^{81} + q^{82} - 2 q^{83} + 2 q^{86} + 2 q^{88} + 2 q^{89} - 2 q^{96} - q^{97} + q^{98} + 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.k.a 2888.k 152.k $2$ $1.441$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
2888.1.k.b 2888.k 152.k $6$ $1.441$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-2}) \) None \(-3\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{3}q^{2}+(-\zeta_{18}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{6}q^{4}+\cdots\)
2888.1.k.c 2888.k 152.k $6$ $1.441$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-2}) \) None \(3\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{3}q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2888, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2888, [\chi]) \cong \)