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Properties

Label 2070.4.bn
Level $2070$
Weight $4$
Character orbit 2070.bn
Rep. character $\chi_{2070}(49,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $8640$
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.bn (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1035 \)
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 8640 17440
Cusp forms 25760 8640 17120
Eisenstein series 320 0 320

Trace form

\( 8640 q - 1728 q^{4} + 16 q^{5} + 16 q^{6} + 100 q^{9} + O(q^{10}) \) \( 8640 q - 1728 q^{4} + 16 q^{5} + 16 q^{6} + 100 q^{9} + 88 q^{11} - 136 q^{14} - 1396 q^{15} + 6912 q^{16} - 64 q^{20} + 104 q^{21} + 32 q^{24} + 288 q^{25} + 28 q^{29} + 1224 q^{30} - 144 q^{31} + 800 q^{36} + 1584 q^{39} + 100 q^{41} + 704 q^{44} - 332 q^{45} - 504 q^{46} - 19386 q^{49} + 752 q^{50} + 64 q^{51} + 2556 q^{54} + 1584 q^{55} + 2480 q^{56} + 1840 q^{59} + 264 q^{60} - 36 q^{61} + 55296 q^{64} + 7288 q^{65} + 4464 q^{66} - 12958 q^{69} + 22320 q^{71} - 224 q^{74} - 7154 q^{75} + 2304 q^{80} - 8324 q^{81} + 2552 q^{84} - 5128 q^{86} + 7688 q^{89} - 456 q^{90} + 1224 q^{94} - 2932 q^{95} - 128 q^{96} - 960 q^{99} + O(q^{100}) \)

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

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