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Properties

Label 2070.4.bg
Level $2070$
Weight $4$
Character orbit 2070.bg
Rep. character $\chi_{2070}(31,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $5760$
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.bg (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{33})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 26080 5760 20320
Cusp forms 25760 5760 20000
Eisenstein series 320 0 320

Trace form

\( 5760 q + 1152 q^{4} + 20 q^{5} - 16 q^{6} - 28 q^{9} + O(q^{10}) \) \( 5760 q + 1152 q^{4} + 20 q^{5} - 16 q^{6} - 28 q^{9} + 88 q^{14} + 4608 q^{16} - 544 q^{17} + 224 q^{18} + 80 q^{20} - 2424 q^{21} - 168 q^{23} + 32 q^{24} + 7200 q^{25} - 320 q^{26} - 1464 q^{27} - 452 q^{29} - 280 q^{30} + 464 q^{33} + 224 q^{36} + 912 q^{38} + 1208 q^{39} - 2020 q^{41} - 304 q^{42} + 760 q^{45} + 504 q^{46} - 1896 q^{47} + 15894 q^{49} + 4896 q^{51} - 2640 q^{53} + 4236 q^{54} - 1584 q^{56} + 5136 q^{57} + 1168 q^{59} + 36 q^{61} - 5616 q^{62} - 7160 q^{63} - 36864 q^{64} + 1040 q^{65} - 304 q^{66} - 10880 q^{68} - 1230 q^{69} + 360 q^{70} + 1280 q^{71} - 4032 q^{72} + 4416 q^{74} + 4336 q^{77} + 2376 q^{78} - 640 q^{80} + 2020 q^{81} - 13344 q^{83} + 4792 q^{84} + 8568 q^{86} - 7564 q^{87} - 2216 q^{89} + 320 q^{90} - 672 q^{92} + 48 q^{93} + 1224 q^{94} + 2080 q^{95} + 128 q^{96} + 14464 q^{98} + 13880 q^{99} + O(q^{100}) \)

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

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