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Properties

Label 1694.4.e
Level $1694$
Weight $4$
Character orbit 1694.e
Rep. character $\chi_{1694}(485,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $436$
Sturm bound $1056$

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Defining parameters

Level: \( N \) \(=\) \( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1694.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1056\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1694, [\chi])\).

Total New Old
Modular forms 1632 436 1196
Cusp forms 1536 436 1100
Eisenstein series 96 0 96

Trace form

\( 436 q + 6 q^{3} - 872 q^{4} + 18 q^{5} + 32 q^{6} - 52 q^{7} - 1980 q^{9} + O(q^{10}) \) \( 436 q + 6 q^{3} - 872 q^{4} + 18 q^{5} + 32 q^{6} - 52 q^{7} - 1980 q^{9} - 32 q^{10} + 24 q^{12} + 96 q^{13} + 72 q^{14} + 84 q^{15} - 3488 q^{16} + 14 q^{17} + 64 q^{18} - 286 q^{19} - 144 q^{20} + 438 q^{21} + 134 q^{23} - 64 q^{24} - 5492 q^{25} + 40 q^{26} + 348 q^{27} + 8 q^{28} - 112 q^{29} - 56 q^{30} - 374 q^{31} - 512 q^{34} + 234 q^{35} + 15840 q^{36} + 962 q^{37} + 16 q^{38} + 468 q^{39} - 128 q^{40} + 512 q^{41} + 600 q^{42} - 1408 q^{43} + 1508 q^{45} - 112 q^{46} - 102 q^{47} - 192 q^{48} + 996 q^{49} - 320 q^{50} + 1194 q^{51} - 192 q^{52} - 58 q^{53} - 1048 q^{54} - 288 q^{56} - 3732 q^{57} + 320 q^{58} + 1734 q^{59} - 168 q^{60} - 1014 q^{61} - 1760 q^{62} - 1492 q^{63} + 27904 q^{64} - 1060 q^{65} - 890 q^{67} + 56 q^{68} + 1468 q^{69} + 496 q^{70} - 4256 q^{71} + 256 q^{72} + 226 q^{73} + 360 q^{74} + 816 q^{75} + 2288 q^{76} + 3584 q^{78} - 2006 q^{79} + 288 q^{80} - 18186 q^{81} + 1568 q^{82} + 4304 q^{83} - 1272 q^{84} + 4444 q^{85} - 200 q^{86} - 2740 q^{87} - 1374 q^{89} - 656 q^{90} - 15936 q^{91} - 1072 q^{92} - 10786 q^{93} - 1608 q^{94} - 2410 q^{95} - 256 q^{96} + 6360 q^{97} - 1392 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1694, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1694, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1694, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(847, [\chi])\)\(^{\oplus 2}\)