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Properties

Label 2070.4.bo
Level $2070$
Weight $4$
Character orbit 2070.bo
Rep. character $\chi_{2070}(11,\cdot)$
Character field $\Q(\zeta_{66})$
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.bo (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{66})\)
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

\( 5760 q - 1152 q^{4} + 16 q^{6} + 28 q^{9} + O(q^{10}) \) \( 5760 q - 1152 q^{4} + 16 q^{6} + 28 q^{9} + 4608 q^{16} - 224 q^{18} + 2640 q^{21} + 504 q^{23} + 32 q^{24} + 7200 q^{25} + 1464 q^{27} - 1356 q^{29} + 224 q^{36} + 1688 q^{39} - 300 q^{41} + 504 q^{46} + 792 q^{47} - 15894 q^{49} + 4236 q^{54} + 5808 q^{56} + 8448 q^{57} - 6000 q^{59} - 8360 q^{63} + 36864 q^{64} - 5456 q^{66} + 2330 q^{69} - 360 q^{70} - 4032 q^{72} - 10032 q^{74} + 8688 q^{77} + 2376 q^{78} + 11268 q^{81} + 56232 q^{83} + 3784 q^{84} + 2332 q^{87} + 2016 q^{92} - 9680 q^{93} + 1224 q^{94} + 6240 q^{95} - 128 q^{96} - 9240 q^{99} + O(q^{100}) \)

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

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