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Properties

Label 2070.4.bj
Level $2070$
Weight $4$
Character orbit 2070.bj
Rep. character $\chi_{2070}(37,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $3600$
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.bj (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 26240 3600 22640
Cusp forms 25600 3600 22000
Eisenstein series 640 0 640

Trace form

\( 3600 q + O(q^{10}) \) \( 3600 q + 192 q^{13} + 5760 q^{16} + 1916 q^{23} - 1168 q^{25} - 304 q^{26} - 352 q^{28} + 256 q^{31} - 688 q^{35} + 2376 q^{37} - 1488 q^{41} - 32 q^{46} + 5192 q^{47} - 272 q^{50} + 768 q^{52} + 1112 q^{55} + 3872 q^{56} - 2112 q^{61} + 1376 q^{62} + 528 q^{70} - 21888 q^{71} - 3600 q^{73} - 3600 q^{77} + 1072 q^{82} + 468 q^{85} + 10472 q^{86} - 80 q^{92} + 15008 q^{95} + 25344 q^{97} + 8400 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)