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Properties

Label 2888.2.p
Level $2888$
Weight $2$
Character orbit 2888.p
Rep. character $\chi_{2888}(429,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $648$
Sturm bound $760$

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Defining parameters

Level: \( N \) \(=\) \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2888.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2888, [\chi])\).

Total New Old
Modular forms 800 712 88
Cusp forms 720 648 72
Eisenstein series 80 64 16

Trace form

\( 648 q + q^{2} - q^{4} + 3 q^{6} + 8 q^{7} - 2 q^{8} + 294 q^{9} + O(q^{10}) \) \( 648 q + q^{2} - q^{4} + 3 q^{6} + 8 q^{7} - 2 q^{8} + 294 q^{9} + 10 q^{10} + 10 q^{12} + 6 q^{15} + 3 q^{16} + 2 q^{17} + 20 q^{18} - 52 q^{20} + 9 q^{22} + 2 q^{23} - 29 q^{24} + 262 q^{25} + 40 q^{26} - 8 q^{28} + 12 q^{30} + 48 q^{31} - 9 q^{32} - 12 q^{33} - 10 q^{34} + 4 q^{36} - 52 q^{39} + 10 q^{40} - 2 q^{41} - 20 q^{42} + 5 q^{44} - 8 q^{46} - 10 q^{47} - 39 q^{48} + 480 q^{49} + 26 q^{50} + 12 q^{52} + 19 q^{54} - 8 q^{55} + 8 q^{56} - 60 q^{58} - 34 q^{60} - 48 q^{62} + 28 q^{63} - 58 q^{64} + 28 q^{65} - 95 q^{66} - 32 q^{68} - 8 q^{70} + 30 q^{71} + 36 q^{72} + 10 q^{73} + 32 q^{78} - 34 q^{79} - 16 q^{80} - 196 q^{81} - 21 q^{82} + 40 q^{84} - 46 q^{86} - 36 q^{87} - 66 q^{88} + 2 q^{89} - 30 q^{90} + 44 q^{92} + 4 q^{94} + 42 q^{96} + 18 q^{97} - 39 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2888, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2888, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2888, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)