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Properties

Label 2888.2.bo
Level $2888$
Weight $2$
Character orbit 2888.bo
Rep. character $\chi_{2888}(9,\cdot)$
Character field $\Q(\zeta_{171})$
Dimension $10260$
Sturm bound $760$

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Defining parameters

Level: \( N \) \(=\) \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2888.bo (of order \(171\) and degree \(108\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 361 \)
Character field: \(\Q(\zeta_{171})\)
Sturm bound: \(760\)

Dimensions

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

Total New Old
Modular forms 41472 10260 31212
Cusp forms 40608 10260 30348
Eisenstein series 864 0 864

Trace form

\( 10260 q - 3 q^{3} + 9 q^{9} + O(q^{10}) \) \( 10260 q - 3 q^{3} + 9 q^{9} + 6 q^{13} - 12 q^{15} + 108 q^{17} + 6 q^{19} + 6 q^{21} - 12 q^{23} - 12 q^{25} + 84 q^{27} + 12 q^{29} + 6 q^{31} + 45 q^{33} + 18 q^{35} - 12 q^{37} + 39 q^{41} + 48 q^{43} + 18 q^{45} + 291 q^{49} - 15 q^{51} + 18 q^{53} + 36 q^{55} - 36 q^{57} - 33 q^{59} + 6 q^{61} + 6 q^{63} - 42 q^{65} - 75 q^{67} + 432 q^{69} - 54 q^{71} - 54 q^{73} - 84 q^{75} - 108 q^{79} - 69 q^{81} - 18 q^{83} + 12 q^{85} - 36 q^{87} - 36 q^{89} + 30 q^{91} - 66 q^{93} + 78 q^{95} + 69 q^{97} + 3 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2888, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(361, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(722, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1444, [\chi])\)\(^{\oplus 2}\)