Properties

Label 2888.1.l
Level $2888$
Weight $1$
Character orbit 2888.l
Rep. character $\chi_{2888}(69,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $380$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2888.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
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 44 36 8
Cusp forms 4 4 0
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 4 0 0 0

Trace form

\( 4 q - 2 q^{4} + 2 q^{6} - 4 q^{7} + O(q^{10}) \) \( 4 q - 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{16} + 2 q^{17} + 2 q^{23} + 2 q^{24} - 2 q^{25} - 4 q^{26} + 2 q^{28} + 4 q^{39} - 2 q^{42} - 4 q^{47} - 2 q^{54} - 4 q^{58} + 4 q^{64} - 4 q^{68} + 2 q^{73} - 4 q^{74} + 2 q^{81} + 4 q^{87} + 2 q^{92} - 4 q^{96} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2888.1.l.a 2888.l 152.l $2$ $1.441$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-38}) \) None 152.1.g.a \(-1\) \(1\) \(0\) \(-2\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
2888.1.l.b 2888.l 152.l $2$ $1.441$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-38}) \) None 152.1.g.a \(1\) \(-1\) \(0\) \(-2\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)