↑

Properties

Label 2070.4.q
Level $2070$
Weight $4$
Character orbit 2070.q
Rep. character $\chi_{2070}(551,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $576$
Sturm bound $1728$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2070.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 2608 576 2032
Cusp forms 2576 576 2000
Eisenstein series 32 0 32

Trace form

\( 576 q + 1152 q^{4} - 16 q^{6} - 28 q^{9} + O(q^{10}) \) \( 576 q + 1152 q^{4} - 16 q^{6} - 28 q^{9} - 4608 q^{16} + 224 q^{18} - 504 q^{23} - 32 q^{24} - 7200 q^{25} - 1200 q^{27} + 1356 q^{29} - 224 q^{36} - 1688 q^{39} + 300 q^{41} - 504 q^{46} - 792 q^{47} + 13716 q^{49} - 1112 q^{54} + 6000 q^{59} - 36864 q^{64} - 2330 q^{69} + 360 q^{70} - 896 q^{72} - 8688 q^{77} + 528 q^{78} - 3524 q^{81} + 7040 q^{87} - 2016 q^{92} + 9680 q^{93} - 1224 q^{94} - 6240 q^{95} + 128 q^{96} + O(q^{100}) \)

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

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