Properties

Label 2888.2.q
Level $2888$
Weight $2$
Character orbit 2888.q
Rep. character $\chi_{2888}(1137,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $510$
Sturm bound $760$

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Defining parameters

Level: \( N \) \(=\) \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2888.q (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(760\)

Dimensions

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

Total New Old
Modular forms 2520 510 2010
Cusp forms 2040 510 1530
Eisenstein series 480 0 480

Trace form

\( 510 q - 3 q^{3} + 9 q^{9} + O(q^{10}) \) \( 510 q - 3 q^{3} + 9 q^{9} + 6 q^{13} - 12 q^{15} - 6 q^{17} + 6 q^{21} - 12 q^{23} - 12 q^{25} + 27 q^{27} + 12 q^{29} + 6 q^{31} + 45 q^{33} + 18 q^{35} - 12 q^{37} + 72 q^{39} + 39 q^{41} + 48 q^{43} + 18 q^{45} - 249 q^{49} - 15 q^{51} + 18 q^{53} + 36 q^{55} - 33 q^{59} + 6 q^{61} + 6 q^{63} - 42 q^{65} - 75 q^{67} - 24 q^{69} - 54 q^{71} - 54 q^{73} - 84 q^{75} - 72 q^{77} - 108 q^{79} - 69 q^{81} + 18 q^{83} + 12 q^{85} - 72 q^{87} - 36 q^{89} - 84 q^{91} - 66 q^{93} + 69 q^{97} + 3 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2888, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(361, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(722, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1444, [\chi])\)\(^{\oplus 2}\)