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Properties

Label 2888.1.bb
Level $2888$
Weight $1$
Character orbit 2888.bb
Rep. character $\chi_{2888}(115,\cdot)$
Character field $\Q(\zeta_{38})$
Dimension $18$
Newform subspaces $1$
Sturm bound $380$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2888.bb (of order \(38\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2888 \)
Character field: \(\Q(\zeta_{38})\)
Newform subspaces: \( 1 \)
Sturm bound: \(380\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 54 54 0
Cusp forms 18 18 0
Eisenstein series 36 36 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 18 0 0 0

Trace form

\( 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9} + O(q^{10}) \) \( 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9} - 2 q^{11} - 2 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - q^{19} - 2 q^{22} - 2 q^{24} - q^{25} + 15 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} + 18 q^{38} - 2 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} - 4 q^{54} - 2 q^{57} - 2 q^{59} - q^{64} - 4 q^{66} - 2 q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} - 2 q^{75} - q^{76} + 14 q^{81} - 2 q^{82} + 17 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99} + O(q^{100}) \)

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.bb.a 2888.bb 2888.ab $18$ $1.441$ \(\Q(\zeta_{38})\) $D_{19}$ \(\Q(\sqrt{-2}) \) None \(-1\) \(17\) \(0\) \(0\) \(q-\zeta_{38}^{3}q^{2}+(1-\zeta_{38}^{17})q^{3}+\zeta_{38}^{6}q^{4}+\cdots\)