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Properties

Label 1694.4.n
Level $1694$
Weight $4$
Character orbit 1694.n
Rep. character $\chi_{1694}(9,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1728$
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.n (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1056\)

Dimensions

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

Total New Old
Modular forms 6528 1728 4800
Cusp forms 6144 1728 4416
Eisenstein series 384 0 384

Trace form

\( 1728 q + 864 q^{4} - 16 q^{5} - 48 q^{6} + 24 q^{7} + 1848 q^{9} + O(q^{10}) \) \( 1728 q + 864 q^{4} - 16 q^{5} - 48 q^{6} + 24 q^{7} + 1848 q^{9} - 136 q^{10} - 104 q^{13} + 52 q^{14} + 12 q^{15} + 3456 q^{16} + 526 q^{17} - 112 q^{18} + 144 q^{19} + 128 q^{20} - 440 q^{21} - 196 q^{23} + 96 q^{24} + 5432 q^{25} + 32 q^{26} - 72 q^{27} - 8 q^{28} + 1252 q^{29} - 48 q^{30} - 414 q^{31} - 1920 q^{34} - 2548 q^{35} - 16064 q^{36} - 720 q^{37} + 248 q^{38} - 1212 q^{39} + 16 q^{40} + 68 q^{41} + 1820 q^{42} + 1680 q^{43} - 1344 q^{45} - 40 q^{46} + 192 q^{47} - 2124 q^{49} + 448 q^{50} + 1060 q^{51} + 208 q^{52} - 952 q^{53} - 3456 q^{54} + 224 q^{56} + 3968 q^{57} + 1344 q^{58} - 1936 q^{59} + 16 q^{60} - 928 q^{61} - 3808 q^{62} - 5956 q^{63} - 27648 q^{64} - 3392 q^{65} + 4512 q^{67} + 2104 q^{68} + 1856 q^{69} + 3012 q^{70} + 3376 q^{71} + 672 q^{72} + 4172 q^{73} + 1568 q^{74} + 4808 q^{75} + 1888 q^{76} + 9920 q^{78} + 4140 q^{79} + 384 q^{80} + 23348 q^{81} - 1560 q^{82} + 464 q^{83} + 1440 q^{84} + 7424 q^{85} + 548 q^{86} + 16 q^{87} + 64 q^{89} - 15504 q^{90} + 10866 q^{91} - 1792 q^{92} + 3956 q^{93} + 2464 q^{94} - 8044 q^{95} + 384 q^{96} - 7788 q^{97} - 1248 q^{98} + O(q^{100}) \)

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

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