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Properties

Label 1694.4.bc
Level $1694$
Weight $4$
Character orbit 1694.bc
Rep. character $\chi_{1694}(25,\cdot)$
Character field $\Q(\zeta_{165})$
Dimension $21120$
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.bc (of order \(165\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{165})\)
Sturm bound: \(1056\)

Dimensions

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

Total New Old
Modular forms 63680 21120 42560
Cusp forms 63040 21120 41920
Eisenstein series 640 0 640

Trace form

\( 21120 q - 1056 q^{4} - 16 q^{5} - 48 q^{6} + 24 q^{7} + 23664 q^{9} + O(q^{10}) \) \( 21120 q - 1056 q^{4} - 16 q^{5} - 48 q^{6} + 24 q^{7} + 23664 q^{9} - 268 q^{10} - 286 q^{11} - 104 q^{13} - 168 q^{14} - 868 q^{15} - 4224 q^{16} + 526 q^{17} - 112 q^{18} + 144 q^{19} + 128 q^{20} - 440 q^{21} + 1216 q^{22} - 196 q^{23} + 96 q^{24} - 6568 q^{25} + 32 q^{26} - 72 q^{27} - 8 q^{28} + 1252 q^{29} - 48 q^{30} - 414 q^{31} + 1218 q^{33} - 2548 q^{35} + 18496 q^{36} + 1296 q^{37} + 248 q^{38} - 1212 q^{39} - 1744 q^{40} + 68 q^{41} + 1916 q^{42} + 1680 q^{43} - 472 q^{44} - 1344 q^{45} - 40 q^{46} + 560 q^{47} + 5764 q^{49} + 448 q^{50} + 1632 q^{51} + 208 q^{52} - 3654 q^{53} - 3456 q^{54} + 3296 q^{55} + 224 q^{56} + 3968 q^{57} + 1008 q^{58} - 2096 q^{59} + 16 q^{60} - 928 q^{61} - 3808 q^{62} + 424 q^{63} + 33792 q^{64} - 3392 q^{65} - 2528 q^{66} - 4176 q^{67} + 2104 q^{68} + 3056 q^{69} + 2148 q^{70} + 3376 q^{71} + 672 q^{72} + 4172 q^{73} + 1568 q^{74} + 5432 q^{75} + 4880 q^{76} + 12948 q^{77} + 448 q^{78} + 444 q^{79} + 384 q^{80} + 218652 q^{81} + 552 q^{82} + 464 q^{83} + 1440 q^{84} + 23968 q^{85} - 252 q^{86} + 16 q^{87} + 176 q^{88} - 11236 q^{89} - 6000 q^{90} + 270 q^{91} - 10416 q^{92} - 14148 q^{93} - 14080 q^{94} - 23180 q^{95} + 384 q^{96} + 708 q^{97} + 2800 q^{98} + 10448 q^{99} + O(q^{100}) \)

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

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