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Properties

Label 735.4.bg
Level $735$
Weight $4$
Character orbit 735.bg
Rep. character $\chi_{735}(16,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1344$
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.bg (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 4080 1344 2736
Cusp forms 3984 1344 2640
Eisenstein series 96 0 96

Trace form

\( 1344 q + 12 q^{3} + 448 q^{4} - 44 q^{7} + 1008 q^{9} + O(q^{10}) \) \( 1344 q + 12 q^{3} + 448 q^{4} - 44 q^{7} + 1008 q^{9} + 40 q^{10} - 28 q^{11} + 144 q^{12} - 8 q^{13} - 136 q^{14} + 1736 q^{16} - 8 q^{17} + 136 q^{19} - 80 q^{20} + 168 q^{21} + 280 q^{22} - 1440 q^{24} + 2800 q^{25} + 348 q^{26} - 216 q^{27} + 516 q^{28} - 336 q^{29} - 92 q^{31} - 140 q^{32} + 264 q^{33} + 3080 q^{34} + 1600 q^{35} - 8064 q^{36} + 1624 q^{37} - 6888 q^{38} + 1176 q^{39} + 480 q^{40} + 568 q^{41} + 108 q^{42} - 616 q^{43} + 9296 q^{44} + 1092 q^{46} + 4784 q^{47} + 16128 q^{48} + 2436 q^{49} + 2184 q^{51} + 11884 q^{52} + 1736 q^{53} - 1520 q^{55} - 1932 q^{56} + 840 q^{57} - 5740 q^{58} - 1012 q^{59} + 2740 q^{61} - 8648 q^{62} - 216 q^{63} - 17584 q^{64} + 420 q^{65} - 684 q^{66} + 84 q^{67} + 2988 q^{68} - 1296 q^{69} + 3020 q^{70} + 336 q^{71} - 4404 q^{73} + 4704 q^{74} + 300 q^{75} - 3944 q^{76} - 6928 q^{77} - 3528 q^{78} - 1540 q^{79} + 320 q^{80} + 9072 q^{81} - 40372 q^{82} - 2584 q^{83} + 60 q^{84} - 1120 q^{85} - 9856 q^{86} + 2088 q^{87} + 9436 q^{88} + 168 q^{89} - 720 q^{90} - 5184 q^{91} + 2800 q^{92} - 420 q^{93} + 36388 q^{94} - 560 q^{95} - 11520 q^{96} + 23168 q^{97} + 3168 q^{98} + 504 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)