Properties

Label 1694.2.e
Level $1694$
Weight $2$
Character orbit 1694.e
Rep. character $\chi_{1694}(485,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $144$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1694.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1694, [\chi])\).

Total New Old
Modular forms 576 144 432
Cusp forms 480 144 336
Eisenstein series 96 0 96

Trace form

\( 144q - 72q^{4} - 4q^{5} - 8q^{6} + 8q^{7} - 64q^{9} + O(q^{10}) \) \( 144q - 72q^{4} - 4q^{5} - 8q^{6} + 8q^{7} - 64q^{9} - 8q^{13} + 8q^{14} - 8q^{15} - 72q^{16} + 12q^{17} - 8q^{18} + 8q^{20} - 16q^{21} - 16q^{23} + 4q^{24} - 72q^{25} - 12q^{26} + 24q^{27} - 4q^{28} - 8q^{29} + 8q^{30} - 4q^{31} + 16q^{34} - 4q^{35} + 128q^{36} - 12q^{37} - 4q^{38} - 4q^{39} + 24q^{41} + 12q^{42} + 40q^{43} + 4q^{45} + 4q^{46} + 12q^{47} - 20q^{49} + 32q^{50} - 12q^{51} + 4q^{52} - 40q^{53} + 16q^{54} - 4q^{56} + 56q^{57} - 24q^{58} + 4q^{59} + 4q^{60} + 36q^{61} - 24q^{62} + 20q^{63} + 144q^{64} - 4q^{65} - 8q^{67} + 12q^{68} - 16q^{69} - 36q^{70} + 8q^{71} - 8q^{72} - 16q^{73} - 12q^{74} - 68q^{75} - 20q^{79} - 4q^{80} - 64q^{81} - 8q^{82} - 40q^{83} - 4q^{84} - 64q^{85} + 4q^{86} + 12q^{87} - 4q^{89} - 72q^{90} + 108q^{91} + 32q^{92} + 92q^{93} - 8q^{94} - 4q^{95} + 4q^{96} - 40q^{97} + 48q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1694, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1694, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1694, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(847, [\chi])\)\(^{\oplus 2}\)