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Properties

Label 2070.3.bq
Level $2070$
Weight $3$
Character orbit 2070.bq
Rep. character $\chi_{2070}(41,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $3840$
Sturm bound $1296$

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Defining parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2070.bq (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2070, [\chi])\).

Total New Old
Modular forms 17440 3840 13600
Cusp forms 17120 3840 13280
Eisenstein series 320 0 320

Trace form

\( 3840 q - 384 q^{4} - 16 q^{6} - 16 q^{9} + O(q^{10}) \) \( 3840 q - 384 q^{4} - 16 q^{6} - 16 q^{9} + 72 q^{14} + 768 q^{16} + 32 q^{18} + 276 q^{21} - 108 q^{23} - 16 q^{24} - 960 q^{25} - 492 q^{27} + 144 q^{29} - 40 q^{30} + 584 q^{33} - 64 q^{36} - 136 q^{39} - 288 q^{41} - 256 q^{42} + 160 q^{45} - 24 q^{46} - 432 q^{47} + 1560 q^{49} - 336 q^{51} - 588 q^{54} - 648 q^{56} - 1356 q^{57} - 360 q^{59} + 96 q^{61} - 956 q^{63} + 3072 q^{64} - 592 q^{66} + 72 q^{69} - 120 q^{70} + 288 q^{72} + 2160 q^{74} + 1368 q^{77} + 1080 q^{78} + 784 q^{81} + 4860 q^{83} + 496 q^{84} - 112 q^{87} + 320 q^{90} - 216 q^{92} + 1080 q^{93} + 168 q^{94} + 720 q^{95} + 32 q^{96} + 392 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2070, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2070, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)