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Properties

Label 2070.4.i
Level $2070$
Weight $4$
Character orbit 2070.i
Rep. character $\chi_{2070}(691,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $528$
Sturm bound $1728$

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Defining parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2070.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2070, [\chi])\).

Total New Old
Modular forms 2608 528 2080
Cusp forms 2576 528 2048
Eisenstein series 32 0 32

Trace form

\( 528 q + 8 q^{2} - 4 q^{3} - 1056 q^{4} - 40 q^{6} + 48 q^{7} - 64 q^{8} - 108 q^{9} + O(q^{10}) \) \( 528 q + 8 q^{2} - 4 q^{3} - 1056 q^{4} - 40 q^{6} + 48 q^{7} - 64 q^{8} - 108 q^{9} + 84 q^{11} + 32 q^{12} - 96 q^{13} - 80 q^{15} - 4224 q^{16} - 152 q^{17} + 368 q^{18} + 840 q^{19} - 224 q^{21} - 72 q^{22} - 160 q^{24} - 6600 q^{25} + 584 q^{27} - 384 q^{28} - 832 q^{29} + 120 q^{31} + 128 q^{32} - 500 q^{33} + 360 q^{34} - 560 q^{35} + 336 q^{36} + 1344 q^{37} + 424 q^{38} - 1024 q^{39} - 20 q^{41} + 516 q^{43} - 672 q^{44} - 64 q^{48} - 13896 q^{49} + 200 q^{50} - 2004 q^{51} - 384 q^{52} + 152 q^{54} + 940 q^{57} - 92 q^{59} - 320 q^{60} + 3360 q^{61} - 3968 q^{62} + 1888 q^{63} + 33792 q^{64} + 1280 q^{65} - 3952 q^{66} + 3900 q^{67} + 304 q^{68} + 1072 q^{71} - 736 q^{72} - 1032 q^{73} - 100 q^{75} - 1680 q^{76} + 2464 q^{77} - 4288 q^{78} - 3552 q^{79} - 172 q^{81} - 4176 q^{82} - 4296 q^{83} + 1792 q^{84} - 1440 q^{85} - 1368 q^{86} + 5008 q^{87} - 288 q^{88} + 10160 q^{89} + 8016 q^{91} - 3104 q^{93} + 1280 q^{96} - 2076 q^{97} - 10000 q^{98} + 1696 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2070, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2070, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)