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Properties

Label 735.4.i
Level $735$
Weight $4$
Character orbit 735.i
Rep. character $\chi_{735}(226,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $160$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 735.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(735, [\chi])\).

Total New Old
Modular forms 704 160 544
Cusp forms 640 160 480
Eisenstein series 64 0 64

Trace form

\( 160 q + 8 q^{2} + 12 q^{3} - 360 q^{4} + 144 q^{8} - 720 q^{9} + O(q^{10}) \) \( 160 q + 8 q^{2} + 12 q^{3} - 360 q^{4} + 144 q^{8} - 720 q^{9} + 40 q^{10} - 108 q^{11} + 144 q^{12} - 8 q^{13} - 1536 q^{16} - 8 q^{17} + 72 q^{18} + 136 q^{19} - 80 q^{20} + 1272 q^{22} - 656 q^{23} - 180 q^{24} - 2000 q^{25} - 716 q^{26} - 216 q^{27} - 1936 q^{29} - 92 q^{31} - 1428 q^{32} + 264 q^{33} + 448 q^{34} + 6480 q^{36} - 332 q^{37} + 56 q^{38} - 252 q^{39} + 480 q^{40} + 1016 q^{41} + 2376 q^{43} - 1016 q^{44} + 1268 q^{46} - 368 q^{47} - 2688 q^{48} - 400 q^{50} + 72 q^{51} + 908 q^{52} - 2904 q^{53} - 1520 q^{55} - 504 q^{57} - 3356 q^{58} - 1376 q^{59} - 2272 q^{61} + 6360 q^{62} + 13600 q^{64} + 420 q^{65} - 684 q^{66} + 1884 q^{67} + 2988 q^{68} - 1296 q^{69} + 4896 q^{71} - 648 q^{72} + 972 q^{73} - 1560 q^{74} + 300 q^{75} - 3944 q^{76} - 1416 q^{78} + 1908 q^{79} + 320 q^{80} - 6480 q^{81} - 332 q^{82} + 2288 q^{83} - 1120 q^{85} - 7668 q^{86} + 2088 q^{87} - 15976 q^{88} - 2072 q^{89} - 720 q^{90} + 35288 q^{92} + 3276 q^{93} + 3292 q^{94} - 640 q^{95} - 1440 q^{96} + 1440 q^{97} + 1944 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(735, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(735, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)